8x^2-6x=4

Solution for 8x^2-6x=4 equation:

8x^2-6x=4

We move all terms to the left:

8x^2-6x-(4)=0

a = 8; b = -6; c = -4;
Δ = b2-4ac
Δ = -62-4·8·(-4)
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{41}}{2*8}=\frac{6-2\sqrt{41}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{41}}{2*8}=\frac{6+2\sqrt{41}}{16}
$