4X(x-2)-(2x-3)2=1-x

Solution for 4X(x-2)-(2x-3)2=1-x equation:

4X(X-2)-(2X-3)2=1-X

We move all terms to the left:

4X(X-2)-(2X-3)2-(1-X)=0

We add all the numbers together, and all the variables

4X(X-2)-(2X-3)2-(-1X+1)=0

We multiply parentheses

4X^2-8X-4X-(-1X+1)+6=0

We get rid of parentheses

4X^2-8X-4X+1X-1+6=0

We add all the numbers together, and all the variables

4X^2-11X+5=0

a = 4; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·4·5
Δ = 41
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{-(-11)-\sqrt{41}}{2*4}=\frac{11-\sqrt{41}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{41}}{2*4}=\frac{11+\sqrt{41}}{8}
$