(-2x^2+18x-2)-(-0.25x+6)=x

Solution for (-2x^2+18x-2)-(-0.25x+6)=x equation:

(-2x^2+18x-2)-(-0.25x+6)=x

We move all terms to the left:

(-2x^2+18x-2)-(-0.25x+6)-(x)=0

We add all the numbers together, and all the variables

(-2x^2+18x-2)-1x-(-0.25x+6)=0

We get rid of parentheses

-2x^2+18x-1x+0.25x-2-6=0

We add all the numbers together, and all the variables

-2x^2+17.25x-8=0

a = -2; b = 17.25; c = -8;
Δ = b2-4ac
Δ = 17.252-4·(-2)·(-8)
Δ = 233.5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17.25)-\sqrt{233.5625}}{2*-2}=\frac{-17.25-\sqrt{233.5625}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17.25)+\sqrt{233.5625}}{2*-2}=\frac{-17.25+\sqrt{233.5625}}{-4}
$