6x^2-14=3x

Solution for 6x^2-14=3x equation:

6x^2-14=3x

We move all terms to the left:

6x^2-14-(3x)=0

a = 6; b = -3; c = -14;
Δ = b2-4ac
Δ = -32-4·6·(-14)
Δ = 345
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{345}}{2*6}=\frac{3-\sqrt{345}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{345}}{2*6}=\frac{3+\sqrt{345}}{12}
$