-7(x-17)x=-35

Solution for -7(x-17)x=-35 equation:

-7(x-17)x=-35

We move all terms to the left:

-7(x-17)x-(-35)=0

We add all the numbers together, and all the variables

-7(x-17)x+35=0

We multiply parentheses

-7x^2+119x+35=0

a = -7; b = 119; c = +35;
Δ = b2-4ac
Δ = 1192-4·(-7)·35
Δ = 15141
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:

$\sqrt{\Delta}=\sqrt{15141}=\sqrt{49*309}=\sqrt{49}*\sqrt{309}=7\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(119)-7\sqrt{309}}{2*-7}=\frac{-119-7\sqrt{309}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(119)+7\sqrt{309}}{2*-7}=\frac{-119+7\sqrt{309}}{-14}
$