3x^2-22x+65=30

Solution for 3x^2-22x+65=30 equation:

3x^2-22x+65=30

We move all terms to the left:

3x^2-22x+65-(30)=0

We add all the numbers together, and all the variables

3x^2-22x+35=0

a = 3; b = -22; c = +35;
Δ = b2-4ac
Δ = -222-4·3·35
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-8}{2*3}=\frac{14}{6}
=2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+8}{2*3}=\frac{30}{6}
=5
$