(3x+7)(5x+8)=12x^2

Solution for (3x+7)(5x+8)=12x^2 equation:

(3x+7)(5x+8)=12x^2

We move all terms to the left:

(3x+7)(5x+8)-(12x^2)=0

determiningTheFunctionDomain
-12x^2+(3x+7)(5x+8)=0

We multiply parentheses ..

-12x^2+(+15x^2+24x+35x+56)=0

We get rid of parentheses

-12x^2+15x^2+24x+35x+56=0

We add all the numbers together, and all the variables

3x^2+59x+56=0

a = 3; b = 59; c = +56;
Δ = b2-4ac
Δ = 592-4·3·56
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-53}{2*3}=\frac{-112}{6}
=-18+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+53}{2*3}=\frac{-6}{6}
=-1
$