2x+8x*x=12

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

2x+8x*x=12

We move all terms to the left:

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

Wy multiply elements

8x^2+2x-12=0

a = 8; b = 2; c = -12;
Δ = b2-4ac
Δ = 22-4·8·(-12)
Δ = 388
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:

$\sqrt{\Delta}=\sqrt{388}=\sqrt{4*97}=\sqrt{4}*\sqrt{97}=2\sqrt{97}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{97}}{2*8}=\frac{-2-2\sqrt{97}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{97}}{2*8}=\frac{-2+2\sqrt{97}}{16}
$