5x^2+33=30x

Solution for 5x^2+33=30x equation:

5x^2+33=30x

We move all terms to the left:

5x^2+33-(30x)=0

a = 5; b = -30; c = +33;
Δ = b2-4ac
Δ = -302-4·5·33
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{15}}{2*5}=\frac{30-4\sqrt{15}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{15}}{2*5}=\frac{30+4\sqrt{15}}{10}
$