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

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

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

We move all terms to the left:

414-((15+x+x)(20+x+x))=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 calculate terms in parentheses: -((+4x^2+40x+30x+300)), so:

(+4x^2+40x+30x+300)

We get rid of parentheses

4x^2+40x+30x+300

We add all the numbers together, and all the variables

4x^2+70x+300

Back to the equation:

-(4x^2+70x+300)


We get rid of parentheses

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