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

Solution for 4(-1+x+2x^2)=0 equation:

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

We multiply parentheses

8x^2+4x-4=0

a = 8; b = 4; c = -4;
Δ = b2-4ac
Δ = 42-4·8·(-4)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*8}=\frac{-16}{16}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*8}=\frac{8}{16}
=1/2
$