X(2x+6)=90

Solution for X(2x+6)=90 equation:

X(2X+6)=90

We move all terms to the left:

X(2X+6)-(90)=0

We multiply parentheses

2X^2+6X-90=0

a = 2; b = 6; c = -90;
Δ = b2-4ac
Δ = 62-4·2·(-90)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-6\sqrt{21}}{2*2}=\frac{-6-6\sqrt{21}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+6\sqrt{21}}{2*2}=\frac{-6+6\sqrt{21}}{4}
$