58=(15+2x)(12+2x)

Solution for 58=(15+2x)(12+2x) equation:

58=(15+2x)(12+2x)

We move all terms to the left:

58-((15+2x)(12+2x))=0

We add all the numbers together, and all the variables

-((2x+15)(2x+12))+58=0

We multiply parentheses ..

-((+4x^2+24x+30x+180))+58=0


We calculate terms in parentheses: -((+4x^2+24x+30x+180)), so:

(+4x^2+24x+30x+180)

We get rid of parentheses

4x^2+24x+30x+180

We add all the numbers together, and all the variables

4x^2+54x+180

Back to the equation:

-(4x^2+54x+180)


We get rid of parentheses

-4x^2-54x-180+58=0

We add all the numbers together, and all the variables

-4x^2-54x-122=0

a = -4; b = -54; c = -122;
Δ = b2-4ac
Δ = -542-4·(-4)·(-122)
Δ = 964
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:

$\sqrt{\Delta}=\sqrt{964}=\sqrt{4*241}=\sqrt{4}*\sqrt{241}=2\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{241}}{2*-4}=\frac{54-2\sqrt{241}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{241}}{2*-4}=\frac{54+2\sqrt{241}}{-8}
$