8(x+7)=6(x-4)12x+21=3(4x+6)

Solution for 8(x+7)=6(x-4)12x+21=3(4x+6) equation:

8(x+7)=6(x-4)12x+21=3(4x+6)

We move all terms to the left:

8(x+7)-(6(x-4)12x+21)=0

We multiply parentheses

8x-(6(x-4)12x+21)+56=0


We calculate terms in parentheses: -(6(x-4)12x+21), so:

6(x-4)12x+21

We multiply parentheses

72x^2-288x+21

Back to the equation:

-(72x^2-288x+21)


We get rid of parentheses

-72x^2+8x+288x-21+56=0

We add all the numbers together, and all the variables

-72x^2+296x+35=0

a = -72; b = 296; c = +35;
Δ = b2-4ac
Δ = 2962-4·(-72)·35
Δ = 97696
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:

$\sqrt{\Delta}=\sqrt{97696}=\sqrt{16*6106}=\sqrt{16}*\sqrt{6106}=4\sqrt{6106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(296)-4\sqrt{6106}}{2*-72}=\frac{-296-4\sqrt{6106}}{-144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(296)+4\sqrt{6106}}{2*-72}=\frac{-296+4\sqrt{6106}}{-144}
$