(3x^2)-15x=48-3x

Solution for (3x^2)-15x=48-3x equation:

(3x^2)-15x=48-3x

We move all terms to the left:

(3x^2)-15x-(48-3x)=0

We add all the numbers together, and all the variables

3x^2-15x-(-3x+48)=0

We get rid of parentheses

3x^2-15x+3x-48=0

We add all the numbers together, and all the variables

3x^2-12x-48=0

a = 3; b = -12; c = -48;
Δ = b2-4ac
Δ = -122-4·3·(-48)
Δ = 720
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:

$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{5}}{2*3}=\frac{12-12\sqrt{5}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{5}}{2*3}=\frac{12+12\sqrt{5}}{6}
$