x(2x+11)+53=90

Solution for x(2x+11)+53=90 equation:

x(2x+11)+53=90

We move all terms to the left:

x(2x+11)+53-(90)=0

We add all the numbers together, and all the variables

x(2x+11)-37=0

We multiply parentheses

2x^2+11x-37=0

a = 2; b = 11; c = -37;
Δ = b2-4ac
Δ = 112-4·2·(-37)
Δ = 417
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-\sqrt{417}}{2*2}=\frac{-11-\sqrt{417}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{417}}{2*2}=\frac{-11+\sqrt{417}}{4}
$