3x^2/2+96=180

Solution for 3x^2/2+96=180 equation:

3x^2/2+96=180

We move all terms to the left:

3x^2/2+96-(180)=0

We add all the numbers together, and all the variables

3x^2/2-84=0

We multiply all the terms by the denominator


3x^2-84*2=0

We add all the numbers together, and all the variables

3x^2-168=0

a = 3; b = 0; c = -168;
Δ = b2-4ac
Δ = 02-4·3·(-168)
Δ = 2016
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:

$\sqrt{\Delta}=\sqrt{2016}=\sqrt{144*14}=\sqrt{144}*\sqrt{14}=12\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{14}}{2*3}=\frac{0-12\sqrt{14}}{6}
=-\frac{12\sqrt{14}}{6}
=-2\sqrt{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{14}}{2*3}=\frac{0+12\sqrt{14}}{6}
=\frac{12\sqrt{14}}{6}
=2\sqrt{14}
$