5x2-19=116

Solution for 5x2-19=116 equation:

5x^2-19=116

We move all terms to the left:

5x^2-19-(116)=0

We add all the numbers together, and all the variables

5x^2-135=0

a = 5; b = 0; c = -135;
Δ = b2-4ac
Δ = 02-4·5·(-135)
Δ = 2700
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:

$\sqrt{\Delta}=\sqrt{2700}=\sqrt{900*3}=\sqrt{900}*\sqrt{3}=30\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{3}}{2*5}=\frac{0-30\sqrt{3}}{10}
=-\frac{30\sqrt{3}}{10}
=-3\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{3}}{2*5}=\frac{0+30\sqrt{3}}{10}
=\frac{30\sqrt{3}}{10}
=3\sqrt{3}
$