76=2x(3x-4)

Solution for 76=2x(3x-4) equation:

76=2x(3x-4)

We move all terms to the left:

76-(2x(3x-4))=0


We calculate terms in parentheses: -(2x(3x-4)), so:

2x(3x-4)

We multiply parentheses

6x^2-8x

Back to the equation:

-(6x^2-8x)


We get rid of parentheses

-6x^2+8x+76=0

a = -6; b = 8; c = +76;
Δ = b2-4ac
Δ = 82-4·(-6)·76
Δ = 1888
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:

$\sqrt{\Delta}=\sqrt{1888}=\sqrt{16*118}=\sqrt{16}*\sqrt{118}=4\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{118}}{2*-6}=\frac{-8-4\sqrt{118}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{118}}{2*-6}=\frac{-8+4\sqrt{118}}{-12}
$