3X2-48x+9=180

Solution for 3X2-48x+9=180 equation:

3X^2-48X+9=180

We move all terms to the left:

3X^2-48X+9-(180)=0

We add all the numbers together, and all the variables

3X^2-48X-171=0

a = 3; b = -48; c = -171;
Δ = b2-4ac
Δ = -482-4·3·(-171)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-66}{2*3}=\frac{-18}{6}
=-3
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+66}{2*3}=\frac{114}{6}
=19
$