-x^2+1-8x=-2-5x^2

Solution for -x^2+1-8x=-2-5x^2 equation:

-x^2+1-8x=-2-5x^2

We move all terms to the left:

-x^2+1-8x-(-2-5x^2)=0

We add all the numbers together, and all the variables

-1x^2-(-2-5x^2)-8x+1=0

We get rid of parentheses

-1x^2+5x^2-8x+2+1=0

We add all the numbers together, and all the variables

4x^2-8x+3=0

a = 4; b = -8; c = +3;
Δ = b2-4ac
Δ = -82-4·4·3
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4}{2*4}=\frac{4}{8}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4}{2*4}=\frac{12}{8}
=1+1/2
$