8x^2+2x=11

Solution for 8x^2+2x=11 equation:

8x^2+2x=11

We move all terms to the left:

8x^2+2x-(11)=0

a = 8; b = 2; c = -11;
Δ = b2-4ac
Δ = 22-4·8·(-11)
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{89}}{2*8}=\frac{-2-2\sqrt{89}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{89}}{2*8}=\frac{-2+2\sqrt{89}}{16}
$