x=(2x+16)(x-6)

Solution for x=(2x+16)(x-6) equation:

x=(2x+16)(x-6)

We move all terms to the left:

x-((2x+16)(x-6))=0

We multiply parentheses ..

-((+2x^2-12x+16x-96))+x=0


We calculate terms in parentheses: -((+2x^2-12x+16x-96)), so:

(+2x^2-12x+16x-96)

We get rid of parentheses

2x^2-12x+16x-96

We add all the numbers together, and all the variables

2x^2+4x-96

Back to the equation:

-(2x^2+4x-96)


We add all the numbers together, and all the variables

x-(2x^2+4x-96)=0

We get rid of parentheses

-2x^2+x-4x+96=0

We add all the numbers together, and all the variables

-2x^2-3x+96=0

a = -2; b = -3; c = +96;
Δ = b2-4ac
Δ = -32-4·(-2)·96
Δ = 777
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{777}}{2*-2}=\frac{3-\sqrt{777}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{777}}{2*-2}=\frac{3+\sqrt{777}}{-4}
$