x2-3x=90

Solution for x2-3x=90 equation:

x2-3x=90

We move all terms to the left:

x2-3x-(90)=0

We add all the numbers together, and all the variables

x^2-3x-90=0

a = 1; b = -3; c = -90;
Δ = b2-4ac
Δ = -32-4·1·(-90)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{41}}{2*1}=\frac{3-3\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{41}}{2*1}=\frac{3+3\sqrt{41}}{2}
$