(2x+45)x=90

Solution for (2x+45)x=90 equation:

(2x+45)x=90

We move all terms to the left:

(2x+45)x-(90)=0

We multiply parentheses

2x^2+45x-90=0

a = 2; b = 45; c = -90;
Δ = b2-4ac
Δ = 452-4·2·(-90)
Δ = 2745
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:

$\sqrt{\Delta}=\sqrt{2745}=\sqrt{9*305}=\sqrt{9}*\sqrt{305}=3\sqrt{305}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-3\sqrt{305}}{2*2}=\frac{-45-3\sqrt{305}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+3\sqrt{305}}{2*2}=\frac{-45+3\sqrt{305}}{4}
$