6x^2-84=3x

Solution for 6x^2-84=3x equation:

6x^2-84=3x

We move all terms to the left:

6x^2-84-(3x)=0

a = 6; b = -3; c = -84;
Δ = b2-4ac
Δ = -32-4·6·(-84)
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-45}{2*6}=\frac{-42}{12}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+45}{2*6}=\frac{48}{12}
=4
$