4-5x^2=-86

Solution for 4-5x^2=-86 equation:

4-5x^2=-86

We move all terms to the left:

4-5x^2-(-86)=0

We add all the numbers together, and all the variables

-5x^2+90=0

a = -5; b = 0; c = +90;
Δ = b2-4ac
Δ = 02-4·(-5)·90
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{2}}{2*-5}=\frac{0-30\sqrt{2}}{-10}
=-\frac{30\sqrt{2}}{-10}
=-\frac{3\sqrt{2}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{2}}{2*-5}=\frac{0+30\sqrt{2}}{-10}
=\frac{30\sqrt{2}}{-10}
=\frac{3\sqrt{2}}{-1}
$