8x2+12x=1

Solution for 8x2+12x=1 equation:

8x^2+12x=1

We move all terms to the left:

8x^2+12x-(1)=0

a = 8; b = 12; c = -1;
Δ = b2-4ac
Δ = 122-4·8·(-1)
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{11}}{2*8}=\frac{-12-4\sqrt{11}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{11}}{2*8}=\frac{-12+4\sqrt{11}}{16}
$