3x^2=9x+45

Solution for 3x^2=9x+45 equation:

3x^2=9x+45

We move all terms to the left:

3x^2-(9x+45)=0

We get rid of parentheses

3x^2-9x-45=0

a = 3; b = -9; c = -45;
Δ = b2-4ac
Δ = -92-4·3·(-45)
Δ = 621
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:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{69}}{2*3}=\frac{9-3\sqrt{69}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{69}}{2*3}=\frac{9+3\sqrt{69}}{6}
$