3x^2-45x=-45

Solution for 3x^2-45x=-45 equation:

3x^2-45x=-45

We move all terms to the left:

3x^2-45x-(-45)=0

We add all the numbers together, and all the variables

3x^2-45x+45=0

a = 3; b = -45; c = +45;
Δ = b2-4ac
Δ = -452-4·3·45
Δ = 1485
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:

$\sqrt{\Delta}=\sqrt{1485}=\sqrt{9*165}=\sqrt{9}*\sqrt{165}=3\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{165}}{2*3}=\frac{45-3\sqrt{165}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{165}}{2*3}=\frac{45+3\sqrt{165}}{6}
$