15x^2=66x+45

Solution for 15x^2=66x+45 equation:

15x^2=66x+45

We move all terms to the left:

15x^2-(66x+45)=0

We get rid of parentheses

15x^2-66x-45=0

a = 15; b = -66; c = -45;
Δ = b2-4ac
Δ = -662-4·15·(-45)
Δ = 7056
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{7056}=84$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-84}{2*15}=\frac{-18}{30}
=-3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+84}{2*15}=\frac{150}{30}
=5
$