60-19x^2=-20

Solution for 60-19x^2=-20 equation:

60-19x^2=-20

We move all terms to the left:

60-19x^2-(-20)=0

We add all the numbers together, and all the variables

-19x^2+80=0

a = -19; b = 0; c = +80;
Δ = b2-4ac
Δ = 02-4·(-19)·80
Δ = 6080
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:

$\sqrt{\Delta}=\sqrt{6080}=\sqrt{64*95}=\sqrt{64}*\sqrt{95}=8\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{95}}{2*-19}=\frac{0-8\sqrt{95}}{-38}
=-\frac{8\sqrt{95}}{-38}
=-\frac{4\sqrt{95}}{-19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{95}}{2*-19}=\frac{0+8\sqrt{95}}{-38}
=\frac{8\sqrt{95}}{-38}
=\frac{4\sqrt{95}}{-19}
$