(5x+10)(4x+9)=90

Solution for (5x+10)(4x+9)=90 equation:

(5x+10)(4x+9)=90

We move all terms to the left:

(5x+10)(4x+9)-(90)=0

We multiply parentheses ..

(+20x^2+45x+40x+90)-90=0

We get rid of parentheses

20x^2+45x+40x+90-90=0

We add all the numbers together, and all the variables

20x^2+85x=0

a = 20; b = 85; c = 0;
Δ = b2-4ac
Δ = 852-4·20·0
Δ = 7225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7225}=85$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(85)-85}{2*20}=\frac{-170}{40}
=-4+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(85)+85}{2*20}=\frac{0}{40}
=0
$