3X2-12x+142=180

Solution for 3X2-12x+142=180 equation:

3X^2-12X+142=180

We move all terms to the left:

3X^2-12X+142-(180)=0

We add all the numbers together, and all the variables

3X^2-12X-38=0

a = 3; b = -12; c = -38;
Δ = b2-4ac
Δ = -122-4·3·(-38)
Δ = 600
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:

$\sqrt{\Delta}=\sqrt{600}=\sqrt{100*6}=\sqrt{100}*\sqrt{6}=10\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-10\sqrt{6}}{2*3}=\frac{12-10\sqrt{6}}{6}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+10\sqrt{6}}{2*3}=\frac{12+10\sqrt{6}}{6}
$