3x^2-63x=-69

Solution for 3x^2-63x=-69 equation:

3x^2-63x=-69

We move all terms to the left:

3x^2-63x-(-69)=0

We add all the numbers together, and all the variables

3x^2-63x+69=0

a = 3; b = -63; c = +69;
Δ = b2-4ac
Δ = -632-4·3·69
Δ = 3141
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:

$\sqrt{\Delta}=\sqrt{3141}=\sqrt{9*349}=\sqrt{9}*\sqrt{349}=3\sqrt{349}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{349}}{2*3}=\frac{63-3\sqrt{349}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{349}}{2*3}=\frac{63+3\sqrt{349}}{6}
$