(4+2x)(5+2x)=90

Solution for (4+2x)(5+2x)=90 equation:

(4+2x)(5+2x)=90

We move all terms to the left:

(4+2x)(5+2x)-(90)=0

We add all the numbers together, and all the variables

(2x+4)(2x+5)-90=0

We multiply parentheses ..

(+4x^2+10x+8x+20)-90=0

We get rid of parentheses

4x^2+10x+8x+20-90=0

We add all the numbers together, and all the variables

4x^2+18x-70=0

a = 4; b = 18; c = -70;
Δ = b2-4ac
Δ = 182-4·4·(-70)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-38}{2*4}=\frac{-56}{8}
=-7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+38}{2*4}=\frac{20}{8}
=2+1/2
$