100=(x+28+x)(x+15+x)

Solution for 100=(x+28+x)(x+15+x) equation:

100=(x+28+x)(x+15+x)

We move all terms to the left:

100-((x+28+x)(x+15+x))=0

We add all the numbers together, and all the variables

-((2x+28)(2x+15))+100=0

We multiply parentheses ..

-((+4x^2+30x+56x+420))+100=0


We calculate terms in parentheses: -((+4x^2+30x+56x+420)), so:

(+4x^2+30x+56x+420)

We get rid of parentheses

4x^2+30x+56x+420

We add all the numbers together, and all the variables

4x^2+86x+420

Back to the equation:

-(4x^2+86x+420)


We get rid of parentheses

-4x^2-86x-420+100=0

We add all the numbers together, and all the variables

-4x^2-86x-320=0

a = -4; b = -86; c = -320;
Δ = b2-4ac
Δ = -862-4·(-4)·(-320)
Δ = 2276
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2276}=\sqrt{4*569}=\sqrt{4}*\sqrt{569}=2\sqrt{569}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-2\sqrt{569}}{2*-4}=\frac{86-2\sqrt{569}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+2\sqrt{569}}{2*-4}=\frac{86+2\sqrt{569}}{-8}
$