111x^2+3=8

Solution for 111x^2+3=8 equation:

111x^2+3=8

We move all terms to the left:

111x^2+3-(8)=0

We add all the numbers together, and all the variables

111x^2-5=0

a = 111; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·111·(-5)
Δ = 2220
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:

$\sqrt{\Delta}=\sqrt{2220}=\sqrt{4*555}=\sqrt{4}*\sqrt{555}=2\sqrt{555}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{555}}{2*111}=\frac{0-2\sqrt{555}}{222}
=-\frac{2\sqrt{555}}{222}
=-\frac{\sqrt{555}}{111}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{555}}{2*111}=\frac{0+2\sqrt{555}}{222}
=\frac{2\sqrt{555}}{222}
=\frac{\sqrt{555}}{111}
$