9x2=-15+48x

Solution for 9x2=-15+48x equation:

9x^2=-15+48x

We move all terms to the left:

9x^2-(-15+48x)=0

We add all the numbers together, and all the variables

9x^2-(48x-15)=0

We get rid of parentheses

9x^2-48x+15=0

a = 9; b = -48; c = +15;
Δ = b2-4ac
Δ = -482-4·9·15
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-42}{2*9}=\frac{6}{18}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+42}{2*9}=\frac{90}{18}
=5
$