(2x)(3x+12=97)

Solution for (2x)(3x+12=97) equation:

(2x)(3x+12=97)

We move all terms to the left:

(2x)(3x+12-(97))=0

We add all the numbers together, and all the variables

2x(3x-85)=0

We multiply parentheses

6x^2-170x=0

a = 6; b = -170; c = 0;
Δ = b2-4ac
Δ = -1702-4·6·0
Δ = 28900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{28900}=170$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-170)-170}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-170)+170}{2*6}=\frac{340}{12}
=28+1/3
$