(x+6)(2x+9)=90

Solution for (x+6)(2x+9)=90 equation:

(x+6)(2x+9)=90

We move all terms to the left:

(x+6)(2x+9)-(90)=0

We multiply parentheses ..

(+2x^2+9x+12x+54)-90=0

We get rid of parentheses

2x^2+9x+12x+54-90=0

We add all the numbers together, and all the variables

2x^2+21x-36=0

a = 2; b = 21; c = -36;
Δ = b2-4ac
Δ = 212-4·2·(-36)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*2}=\frac{-48}{4}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*2}=\frac{6}{4}
=1+1/2
$