Simplify \(3{x}^{2}-24x+48-5{x}^{2}+36x-45\) to \(-2{x}^{2}+12x+3\).
\[-2{x}^{2}+12x+3=8{x}^{2}-22x+5-40\]
Simplify \(8{x}^{2}-22x+5-40\) to \(8{x}^{2}-22x-35\).
\[-2{x}^{2}+12x+3=8{x}^{2}-22x-35\]
Move all terms to one side.
\[2{x}^{2}-12x-3+8{x}^{2}-22x-35=0\]
Simplify \(2{x}^{2}-12x-3+8{x}^{2}-22x-35\) to \(10{x}^{2}-34x-38\).
\[10{x}^{2}-34x-38=0\]
Use the Quadratic Formula.
In general, given \(a{x}^{2}+bx+c=0\), there exists two solutions where:
\[x=\frac{-b+\sqrt{{b}^{2}-4ac}}{2a},\frac{-b-\sqrt{{b}^{2}-4ac}}{2a}\]
In this case, \(a=10\), \(b=-34\) and \(c=-38\).
\[{x}^{}=\frac{34+\sqrt{{(-34)}^{2}-4\times 10\times -38}}{2\times 10},\frac{34-\sqrt{{(-34)}^{2}-4\times 10\times -38}}{2\times 10}\]
Simplify.
\[x=\frac{34+2\sqrt{669}}{20},\frac{34-2\sqrt{669}}{20}\]
\[x=\frac{34+2\sqrt{669}}{20},\frac{34-2\sqrt{669}}{20}\]
Simplify solutions.
\[x=\frac{17+\sqrt{669}}{10},\frac{17-\sqrt{669}}{10}\]
Decimal Form: 4.286503, -0.886503
x=(17+sqrt(669))/10,(17-sqrt(669))/10
