x^2-35x+250=1500

Solution for x^2-35x+250=1500 equation:

x^2-35x+250=1500

We move all terms to the left:

x^2-35x+250-(1500)=0

We add all the numbers together, and all the variables

x^2-35x-1250=0

a = 1; b = -35; c = -1250;
Δ = b2-4ac
Δ = -352-4·1·(-1250)
Δ = 6225
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:

$\sqrt{\Delta}=\sqrt{6225}=\sqrt{25*249}=\sqrt{25}*\sqrt{249}=5\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{249}}{2*1}=\frac{35-5\sqrt{249}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{249}}{2*1}=\frac{35+5\sqrt{249}}{2}
$