6x2=22x+84

Solution for 6x2=22x+84 equation:

6x^2=22x+84

We move all terms to the left:

6x^2-(22x+84)=0

We get rid of parentheses

6x^2-22x-84=0

a = 6; b = -22; c = -84;
Δ = b2-4ac
Δ = -222-4·6·(-84)
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-50}{2*6}=\frac{-28}{12}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+50}{2*6}=\frac{72}{12}
=6
$