5x-17(x-5)(x-2)=0

Solution for 5x-17(x-5)(x-2)=0 equation:

5x-17(x-5)(x-2)=0

We multiply parentheses ..

-17(+x^2-2x-5x+10)+5x=0

We multiply parentheses

-17x^2+34x+85x+5x-170=0

We add all the numbers together, and all the variables

-17x^2+124x-170=0

a = -17; b = 124; c = -170;
Δ = b2-4ac
Δ = 1242-4·(-17)·(-170)
Δ = 3816
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:

$\sqrt{\Delta}=\sqrt{3816}=\sqrt{36*106}=\sqrt{36}*\sqrt{106}=6\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(124)-6\sqrt{106}}{2*-17}=\frac{-124-6\sqrt{106}}{-34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(124)+6\sqrt{106}}{2*-17}=\frac{-124+6\sqrt{106}}{-34}
$