(10+2x)(24+2x)=1176

Solution for (10+2x)(24+2x)=1176 equation:

(10+2x)(24+2x)=1176

We move all terms to the left:

(10+2x)(24+2x)-(1176)=0

We add all the numbers together, and all the variables

(2x+10)(2x+24)-1176=0

We multiply parentheses ..

(+4x^2+48x+20x+240)-1176=0

We get rid of parentheses

4x^2+48x+20x+240-1176=0

We add all the numbers together, and all the variables

4x^2+68x-936=0

a = 4; b = 68; c = -936;
Δ = b2-4ac
Δ = 682-4·4·(-936)
Δ = 19600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{19600}=140$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-140}{2*4}=\frac{-208}{8}
=-26
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+140}{2*4}=\frac{72}{8}
=9
$