3x^2=22x-24

Solution for 3x^2=22x-24 equation:

3x^2=22x-24

We move all terms to the left:

3x^2-(22x-24)=0

We get rid of parentheses

3x^2-22x+24=0

a = 3; b = -22; c = +24;
Δ = b2-4ac
Δ = -222-4·3·24
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-14}{2*3}=\frac{8}{6}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+14}{2*3}=\frac{36}{6}
=6
$