4x^2+3=-x^2+8

Solution for 4x^2+3=-x^2+8 equation:

4x^2+3=-x^2+8

We move all terms to the left:

4x^2+3-(-x^2+8)=0

We get rid of parentheses

4x^2+x^2-8+3=0

We add all the numbers together, and all the variables

5x^2-5=0

a = 5; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·5·(-5)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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