-2x(x-17)=-20x-38

Solution for -2x(x-17)=-20x-38 equation:

-2x(x-17)=-20x-38

We move all terms to the left:

-2x(x-17)-(-20x-38)=0

We multiply parentheses

-2x^2+34x-(-20x-38)=0

We get rid of parentheses

-2x^2+34x+20x+38=0

We add all the numbers together, and all the variables

-2x^2+54x+38=0

a = -2; b = 54; c = +38;
Δ = b2-4ac
Δ = 542-4·(-2)·38
Δ = 3220
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3220}=\sqrt{4*805}=\sqrt{4}*\sqrt{805}=2\sqrt{805}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-2\sqrt{805}}{2*-2}=\frac{-54-2\sqrt{805}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+2\sqrt{805}}{2*-2}=\frac{-54+2\sqrt{805}}{-4}
$