(15+2x)(10+2x)-15(10)=350

Solution for (15+2x)(10+2x)-15(10)=350 equation:

(15+2x)(10+2x)-15(10)=350

We move all terms to the left:

(15+2x)(10+2x)-15(10)-(350)=0

We add all the numbers together, and all the variables

(2x+15)(2x+10)-1510-350=0

We add all the numbers together, and all the variables

(2x+15)(2x+10)-1860=0

We multiply parentheses ..

(+4x^2+20x+30x+150)-1860=0

We get rid of parentheses

4x^2+20x+30x+150-1860=0

We add all the numbers together, and all the variables

4x^2+50x-1710=0

a = 4; b = 50; c = -1710;
Δ = b2-4ac
Δ = 502-4·4·(-1710)
Δ = 29860
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:

$\sqrt{\Delta}=\sqrt{29860}=\sqrt{4*7465}=\sqrt{4}*\sqrt{7465}=2\sqrt{7465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{7465}}{2*4}=\frac{-50-2\sqrt{7465}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{7465}}{2*4}=\frac{-50+2\sqrt{7465}}{8}
$