8x(3x-3)=43

Solution for 8x(3x-3)=43 equation:

8x(3x-3)=43

We move all terms to the left:

8x(3x-3)-(43)=0

We multiply parentheses

24x^2-24x-43=0

a = 24; b = -24; c = -43;
Δ = b2-4ac
Δ = -242-4·24·(-43)
Δ = 4704
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:

$\sqrt{\Delta}=\sqrt{4704}=\sqrt{784*6}=\sqrt{784}*\sqrt{6}=28\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-28\sqrt{6}}{2*24}=\frac{24-28\sqrt{6}}{48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+28\sqrt{6}}{2*24}=\frac{24+28\sqrt{6}}{48}
$