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

Solution for 4x+1=2x^2+7x-1 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = -3; c = +2;
Δ = b2-4ac
Δ = -32-4·(-2)·2
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*-2}=\frac{-2}{-4}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+5}{2*-2}=\frac{8}{-4}
=-2
$