5x2-3=x2+78

Solution for 5x2-3=x2+78 equation:

5x^2-3=x2+78

We move all terms to the left:

5x^2-3-(x2+78)=0

We add all the numbers together, and all the variables

5x^2-(+x^2+78)-3=0

We get rid of parentheses

5x^2-x^2-78-3=0

We add all the numbers together, and all the variables

4x^2-81=0

a = 4; b = 0; c = -81;
Δ = b2-4ac
Δ = 02-4·4·(-81)
Δ = 1296
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1296}=36$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-36}{2*4}=\frac{-36}{8}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+36}{2*4}=\frac{36}{8}
=4+1/2
$