(15+2x)(20+2x)=414

Solution for (15+2x)(20+2x)=414 equation:

(15+2x)(20+2x)=414

We move all terms to the left:

(15+2x)(20+2x)-(414)=0

We add all the numbers together, and all the variables

(2x+15)(2x+20)-414=0

We multiply parentheses ..

(+4x^2+40x+30x+300)-414=0

We get rid of parentheses

4x^2+40x+30x+300-414=0

We add all the numbers together, and all the variables

4x^2+70x-114=0

a = 4; b = 70; c = -114;
Δ = b2-4ac
Δ = 702-4·4·(-114)
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-82}{2*4}=\frac{-152}{8}
=-19
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+82}{2*4}=\frac{12}{8}
=1+1/2
$