33.5x2+36=180

Solution for 33.5x2+36=180 equation:

33.5x^2+36=180

We move all terms to the left:

33.5x^2+36-(180)=0

We add all the numbers together, and all the variables

33.5x^2-144=0

a = 33.5; b = 0; c = -144;
Δ = b2-4ac
Δ = 02-4·33.5·(-144)
Δ = 19296
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:

$\sqrt{\Delta}=\sqrt{19296}=\sqrt{144*134}=\sqrt{144}*\sqrt{134}=12\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{134}}{2*33.5}=\frac{0-12\sqrt{134}}{67}
=-\frac{12\sqrt{134}}{67}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{134}}{2*33.5}=\frac{0+12\sqrt{134}}{67}
=\frac{12\sqrt{134}}{67}
$