2x+8=4x^2-x+7

Solution for 2x+8=4x^2-x+7 equation:

2x+8=4x^2-x+7

We move all terms to the left:

2x+8-(4x^2-x+7)=0

We get rid of parentheses

-4x^2+2x+x-7+8=0

We add all the numbers together, and all the variables

-4x^2+3x+1=0

a = -4; b = 3; c = +1;
Δ = b2-4ac
Δ = 32-4·(-4)·1
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-5}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+5}{2*-4}=\frac{2}{-8}
=-1/4
$