8x^2=12x+2

Solution for 8x^2=12x+2 equation:

8x^2=12x+2

We move all terms to the left:

8x^2-(12x+2)=0

We get rid of parentheses

8x^2-12x-2=0

a = 8; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·8·(-2)
Δ = 208
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:

$\sqrt{\Delta}=\sqrt{208}=\sqrt{16*13}=\sqrt{16}*\sqrt{13}=4\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-4\sqrt{13}}{2*8}=\frac{12-4\sqrt{13}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+4\sqrt{13}}{2*8}=\frac{12+4\sqrt{13}}{16}
$