-4x2+x+1=-7x+1

Solution for -4x2+x+1=-7x+1 equation:

-4x^2+x+1=-7x+1

We move all terms to the left:

-4x^2+x+1-(-7x+1)=0

We get rid of parentheses

-4x^2+x+7x-1+1=0

We add all the numbers together, and all the variables

-4x^2+8x=0

a = -4; b = 8; c = 0;
Δ = b2-4ac
Δ = 82-4·(-4)·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8}{2*-4}=\frac{-16}{-8}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8}{2*-4}=\frac{0}{-8}
=0
$