19x^2+5=180

Solution for 19x^2+5=180 equation:

19x^2+5=180

We move all terms to the left:

19x^2+5-(180)=0

We add all the numbers together, and all the variables

19x^2-175=0

a = 19; b = 0; c = -175;
Δ = b2-4ac
Δ = 02-4·19·(-175)
Δ = 13300
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:

$\sqrt{\Delta}=\sqrt{13300}=\sqrt{100*133}=\sqrt{100}*\sqrt{133}=10\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{133}}{2*19}=\frac{0-10\sqrt{133}}{38}
=-\frac{10\sqrt{133}}{38}
=-\frac{5\sqrt{133}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{133}}{2*19}=\frac{0+10\sqrt{133}}{38}
=\frac{10\sqrt{133}}{38}
=\frac{5\sqrt{133}}{19}
$