8x^2+1=191+3x^2

Solution for 8x^2+1=191+3x^2 equation:

8x^2+1=191+3x^2

We move all terms to the left:

8x^2+1-(191+3x^2)=0

We get rid of parentheses

8x^2-3x^2-191+1=0

We add all the numbers together, and all the variables

5x^2-190=0

a = 5; b = 0; c = -190;
Δ = b2-4ac
Δ = 02-4·5·(-190)
Δ = 3800
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:

$\sqrt{\Delta}=\sqrt{3800}=\sqrt{100*38}=\sqrt{100}*\sqrt{38}=10\sqrt{38}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{38}}{2*5}=\frac{0-10\sqrt{38}}{10}
=-\frac{10\sqrt{38}}{10}
=-\sqrt{38}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{38}}{2*5}=\frac{0+10\sqrt{38}}{10}
=\frac{10\sqrt{38}}{10}
=\sqrt{38}
$