14x^2+8=86x

Solution for 14x^2+8=86x equation:

14x^2+8=86x

We move all terms to the left:

14x^2+8-(86x)=0

a = 14; b = -86; c = +8;
Δ = b2-4ac
Δ = -862-4·14·8
Δ = 6948
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:

$\sqrt{\Delta}=\sqrt{6948}=\sqrt{36*193}=\sqrt{36}*\sqrt{193}=6\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-86)-6\sqrt{193}}{2*14}=\frac{86-6\sqrt{193}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-86)+6\sqrt{193}}{2*14}=\frac{86+6\sqrt{193}}{28}
$