x(2x+11)=90

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

x(2x+11)=90

We move all terms to the left:

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

We multiply parentheses

2x^2+11x-90=0

a = 2; b = 11; c = -90;
Δ = b2-4ac
Δ = 112-4·2·(-90)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-29}{2*2}=\frac{-40}{4}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+29}{2*2}=\frac{18}{4}
=4+1/2
$