x(x-42)=90

Solution for x(x-42)=90 equation:

x(x-42)=90

We move all terms to the left:

x(x-42)-(90)=0

We multiply parentheses

x^2-42x-90=0

a = 1; b = -42; c = -90;
Δ = b2-4ac
Δ = -422-4·1·(-90)
Δ = 2124
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:

$\sqrt{\Delta}=\sqrt{2124}=\sqrt{36*59}=\sqrt{36}*\sqrt{59}=6\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-6\sqrt{59}}{2*1}=\frac{42-6\sqrt{59}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+6\sqrt{59}}{2*1}=\frac{42+6\sqrt{59}}{2}
$