X(x-35)=500

Solution for X(x-35)=500 equation:

X(X-35)=500

We move all terms to the left:

X(X-35)-(500)=0

We multiply parentheses

X^2-35X-500=0

a = 1; b = -35; c = -500;
Δ = b2-4ac
Δ = -352-4·1·(-500)
Δ = 3225
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:

$\sqrt{\Delta}=\sqrt{3225}=\sqrt{25*129}=\sqrt{25}*\sqrt{129}=5\sqrt{129}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{129}}{2*1}=\frac{35-5\sqrt{129}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{129}}{2*1}=\frac{35+5\sqrt{129}}{2}
$