3x^2+54x-22=50

Solution for 3x^2+54x-22=50 equation:

3x^2+54x-22=50

We move all terms to the left:

3x^2+54x-22-(50)=0

We add all the numbers together, and all the variables

3x^2+54x-72=0

a = 3; b = 54; c = -72;
Δ = b2-4ac
Δ = 542-4·3·(-72)
Δ = 3780
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:

$\sqrt{\Delta}=\sqrt{3780}=\sqrt{36*105}=\sqrt{36}*\sqrt{105}=6\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(54)-6\sqrt{105}}{2*3}=\frac{-54-6\sqrt{105}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(54)+6\sqrt{105}}{2*3}=\frac{-54+6\sqrt{105}}{6}
$