8x(x-6)=34

Solution for 8x(x-6)=34 equation:

8x(x-6)=34

We move all terms to the left:

8x(x-6)-(34)=0

We multiply parentheses

8x^2-48x-34=0

a = 8; b = -48; c = -34;
Δ = b2-4ac
Δ = -482-4·8·(-34)
Δ = 3392
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:

$\sqrt{\Delta}=\sqrt{3392}=\sqrt{64*53}=\sqrt{64}*\sqrt{53}=8\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{53}}{2*8}=\frac{48-8\sqrt{53}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{53}}{2*8}=\frac{48+8\sqrt{53}}{16}
$