x^2-18x=75

Solution for x^2-18x=75 equation:

x^2-18x=75

We move all terms to the left:

x^2-18x-(75)=0

a = 1; b = -18; c = -75;
Δ = b2-4ac
Δ = -182-4·1·(-75)
Δ = 624
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:

$\sqrt{\Delta}=\sqrt{624}=\sqrt{16*39}=\sqrt{16}*\sqrt{39}=4\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{39}}{2*1}=\frac{18-4\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{39}}{2*1}=\frac{18+4\sqrt{39}}{2}
$