4x^2-x-0.5=1

Solution for 4x^2-x-0.5=1 equation:

4x^2-x-0.5=1

We move all terms to the left:

4x^2-x-0.5-(1)=0

We add all the numbers together, and all the variables

4x^2-1x-1.5=0

a = 4; b = -1; c = -1.5;
Δ = b2-4ac
Δ = -12-4·4·(-1.5)
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{-(-1)-5}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*4}=\frac{6}{8}
=3/4
$