3x(2x+12)=2(2x+7)

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

3x(2x+12)=2(2x+7)

We move all terms to the left:

3x(2x+12)-(2(2x+7))=0

We multiply parentheses

6x^2+36x-(2(2x+7))=0


We calculate terms in parentheses: -(2(2x+7)), so:

2(2x+7)

We multiply parentheses

4x+14

Back to the equation:

-(4x+14)


We get rid of parentheses

6x^2+36x-4x-14=0

We add all the numbers together, and all the variables

6x^2+32x-14=0

a = 6; b = 32; c = -14;
Δ = b2-4ac
Δ = 322-4·6·(-14)
Δ = 1360
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:

$\sqrt{\Delta}=\sqrt{1360}=\sqrt{16*85}=\sqrt{16}*\sqrt{85}=4\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-4\sqrt{85}}{2*6}=\frac{-32-4\sqrt{85}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+4\sqrt{85}}{2*6}=\frac{-32+4\sqrt{85}}{12}
$