Solve -2(x)^(2)-5\times+3=0 | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

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

Solve for x (complex solution)

$x=-\frac{\sqrt{30}i}{2}\approx -0-2.738612788i$
$x=\frac{\sqrt{30}i}{2}\approx 2.738612788i$

Steps by Finding Square Root

Steps Using the Quadratic Formula

Steps by Finding Square Root

Multiply $5$ and $3$ to get $15$.

$$-2x^{2}-15=0$$

Add $15$ to both sides. Anything plus zero gives itself.

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

Divide both sides by $-2$.

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

The equation is now solved.

$$x=\frac{\sqrt{30}i}{2}$$ $$x=-\frac{\sqrt{30}i}{2}$$

Steps Using the Quadratic Formula

Multiply $5$ and $3$ to get $15$.

$$-2x^{2}-15=0$$

This equation is in standard form: $ax^{2}+bx+c=0$. Substitute $-2$ for $a$, $0$ for $b$, and $-15$ for $c$ in the quadratic formula, $\frac{-b±\sqrt{b^{2}-4ac}}{2a}$.

$$x=\frac{0±\sqrt{0^{2}-4\left(-2\right)\left(-15\right)}}{2\left(-2\right)}$$

Square $0$.

$$x=\frac{0±\sqrt{-4\left(-2\right)\left(-15\right)}}{2\left(-2\right)}$$

Multiply $-4$ times $-2$.

$$x=\frac{0±\sqrt{8\left(-15\right)}}{2\left(-2\right)}$$

Multiply $8$ times $-15$.

$$x=\frac{0±\sqrt{-120}}{2\left(-2\right)}$$

Take the square root of $-120$.

$$x=\frac{0±2\sqrt{30}i}{2\left(-2\right)}$$

Multiply $2$ times $-2$.

$$x=\frac{0±2\sqrt{30}i}{-4}$$

Now solve the equation $x=\frac{0±2\sqrt{30}i}{-4}$ when $±$ is plus.

$$x=-\frac{\sqrt{30}i}{2}$$

Now solve the equation $x=\frac{0±2\sqrt{30}i}{-4}$ when $±$ is minus.

$$x=\frac{\sqrt{30}i}{2}$$

The equation is now solved.

$$x=-\frac{\sqrt{30}i}{2}$$ $$x=\frac{\sqrt{30}i}{2}$$