$$-5x^{2}-15x+7=0$$

$$x=\frac{-\left(-15\right)±\sqrt{\left(-15\right)^{2}-4\left(-5\right)\times 7}}{2\left(-5\right)}$$

$$x=\frac{-\left(-15\right)±\sqrt{225-4\left(-5\right)\times 7}}{2\left(-5\right)}$$

$$x=\frac{-\left(-15\right)±\sqrt{225+20\times 7}}{2\left(-5\right)}$$

$$x=\frac{-\left(-15\right)±\sqrt{225+140}}{2\left(-5\right)}$$

$$x=\frac{-\left(-15\right)±\sqrt{365}}{2\left(-5\right)}$$

$$x=\frac{15±\sqrt{365}}{2\left(-5\right)}$$

$$x=\frac{15±\sqrt{365}}{-10}$$

$$x=\frac{\sqrt{365}+15}{-10}$$

$$x=-\frac{\sqrt{365}}{10}-\frac{3}{2}$$

$$x=\frac{15-\sqrt{365}}{-10}$$

$$x=\frac{\sqrt{365}}{10}-\frac{3}{2}$$

$$x=-\frac{\sqrt{365}}{10}-\frac{3}{2}$$ $$x=\frac{\sqrt{365}}{10}-\frac{3}{2}$$

$$-5x^{2}-15x+7=0$$

$$-5x^{2}-15x+7-7=-7$$

$$-5x^{2}-15x=-7$$

$$\frac{-5x^{2}-15x}{-5}=-\frac{7}{-5}$$

$$x^{2}+\left(-\frac{15}{-5}\right)x=-\frac{7}{-5}$$

$$x^{2}+3x=-\frac{7}{-5}$$

$$x^{2}+3x=\frac{7}{5}$$

$$x^{2}+3x+\left(\frac{3}{2}\right)^{2}=\frac{7}{5}+\left(\frac{3}{2}\right)^{2}$$

$$x^{2}+3x+\frac{9}{4}=\frac{7}{5}+\frac{9}{4}$$

$$x^{2}+3x+\frac{9}{4}=\frac{73}{20}$$

$$\left(x+\frac{3}{2}\right)^{2}=\frac{73}{20}$$

$$\sqrt{\left(x+\frac{3}{2}\right)^{2}}=\sqrt{\frac{73}{20}}$$

$$x+\frac{3}{2}=\frac{\sqrt{365}}{10}$$ $$x+\frac{3}{2}=-\frac{\sqrt{365}}{10}$$

$$x=\frac{\sqrt{365}}{10}-\frac{3}{2}$$ $$x=-\frac{\sqrt{365}}{10}-\frac{3}{2}$$

$$x ^ 2 +3x -\frac{7}{5} = 0$$

$$r + s = -3 $$ $$ rs = -\frac{7}{5}$$

$$r = -\frac{3}{2} - u$$ $$s = -\frac{3}{2} + u$$

$$(-\frac{3}{2} - u) (-\frac{3}{2} + u) = -\frac{7}{5}$$

$$\frac{9}{4} - u^2 = -\frac{7}{5}$$

$$-u^2 = -\frac{7}{5}-\frac{9}{4} = -\frac{73}{20}$$

$$u^2 = \frac{73}{20}$$ $$u = \pm\sqrt{\frac{73}{20}} = \pm \frac{\sqrt{73}}{\sqrt{20}} $$

$$r =-\frac{3}{2} - \frac{\sqrt{73}}{\sqrt{20}} = -3.410$$ $$s = -\frac{3}{2} + \frac{\sqrt{73}}{\sqrt{20}} = 0.410$$