2x(x+51)=90

Solution for 2x(x+51)=90 equation:

2x(x+51)=90

We move all terms to the left:

2x(x+51)-(90)=0

We multiply parentheses

2x^2+102x-90=0

a = 2; b = 102; c = -90;
Δ = b2-4ac
Δ = 1022-4·2·(-90)
Δ = 11124
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:

$\sqrt{\Delta}=\sqrt{11124}=\sqrt{36*309}=\sqrt{36}*\sqrt{309}=6\sqrt{309}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(102)-6\sqrt{309}}{2*2}=\frac{-102-6\sqrt{309}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(102)+6\sqrt{309}}{2*2}=\frac{-102+6\sqrt{309}}{4}
$