86x=12x^2+14

Solution for 86x=12x^2+14 equation:

86x=12x^2+14

We move all terms to the left:

86x-(12x^2+14)=0

We get rid of parentheses

-12x^2+86x-14=0

a = -12; b = 86; c = -14;
Δ = b2-4ac
Δ = 862-4·(-12)·(-14)
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(86)-82}{2*-12}=\frac{-168}{-24}
=+7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(86)+82}{2*-12}=\frac{-4}{-24}
=1/6
$