8x(2x-3)=12(3x+7)-7

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

8x(2x-3)=12(3x+7)-7

We move all terms to the left:

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

We multiply parentheses

16x^2-24x-(12(3x+7)-7)=0


We calculate terms in parentheses: -(12(3x+7)-7), so:

12(3x+7)-7

We multiply parentheses

36x+84-7

We add all the numbers together, and all the variables

36x+77

Back to the equation:

-(36x+77)


We get rid of parentheses

16x^2-24x-36x-77=0

We add all the numbers together, and all the variables

16x^2-60x-77=0

a = 16; b = -60; c = -77;
Δ = b2-4ac
Δ = -602-4·16·(-77)
Δ = 8528
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:

$\sqrt{\Delta}=\sqrt{8528}=\sqrt{16*533}=\sqrt{16}*\sqrt{533}=4\sqrt{533}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{533}}{2*16}=\frac{60-4\sqrt{533}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{533}}{2*16}=\frac{60+4\sqrt{533}}{32}
$