3x^2-30x+57=0

Solution for 3x^2-30x+57=0 equation:

3x^2-30x+57=0

a = 3; b = -30; c = +57;
Δ = b2-4ac
Δ = -302-4·3·57
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{6}}{2*3}=\frac{30-6\sqrt{6}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{6}}{2*3}=\frac{30+6\sqrt{6}}{6}
$