3x^2-48x+4=188

Solution for 3x^2-48x+4=188 equation:

3x^2-48x+4=188

We move all terms to the left:

3x^2-48x+4-(188)=0

We add all the numbers together, and all the variables

3x^2-48x-184=0

a = 3; b = -48; c = -184;
Δ = b2-4ac
Δ = -482-4·3·(-184)
Δ = 4512
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:

$\sqrt{\Delta}=\sqrt{4512}=\sqrt{16*282}=\sqrt{16}*\sqrt{282}=4\sqrt{282}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{282}}{2*3}=\frac{48-4\sqrt{282}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{282}}{2*3}=\frac{48+4\sqrt{282}}{6}
$