2x(x+21)=90

Solution for 2x(x+21)=90 equation:

2x(x+21)=90

We move all terms to the left:

2x(x+21)-(90)=0

We multiply parentheses

2x^2+42x-90=0

a = 2; b = 42; c = -90;
Δ = b2-4ac
Δ = 422-4·2·(-90)
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-6\sqrt{69}}{2*2}=\frac{-42-6\sqrt{69}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+6\sqrt{69}}{2*2}=\frac{-42+6\sqrt{69}}{4}
$