3x^2-30x=-69

Solution for 3x^2-30x=-69 equation:

3x^2-30x=-69

We move all terms to the left:

3x^2-30x-(-69)=0

We add all the numbers together, and all the variables

3x^2-30x+69=0

a = 3; b = -30; c = +69;
Δ = b2-4ac
Δ = -302-4·3·69
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{2}}{2*3}=\frac{30-6\sqrt{2}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{2}}{2*3}=\frac{30+6\sqrt{2}}{6}
$