6x^2-4=22x

Solution for 6x^2-4=22x equation:

6x^2-4=22x

We move all terms to the left:

6x^2-4-(22x)=0

a = 6; b = -22; c = -4;
Δ = b2-4ac
Δ = -222-4·6·(-4)
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{145}}{2*6}=\frac{22-2\sqrt{145}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{145}}{2*6}=\frac{22+2\sqrt{145}}{12}
$