4(2x-1)=3x-x2

Solution for 4(2x-1)=3x-x2 equation:

4(2x-1)=3x-x2

We move all terms to the left:

4(2x-1)-(3x-x2)=0

We add all the numbers together, and all the variables

-(+3x-1x^2)+4(2x-1)=0

We multiply parentheses

-(+3x-1x^2)+8x-4=0

We get rid of parentheses

1x^2-3x+8x-4=0

We add all the numbers together, and all the variables

x^2+5x-4=0

a = 1; b = 5; c = -4;
Δ = b2-4ac
Δ = 52-4·1·(-4)
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{-(5)-\sqrt{41}}{2*1}=\frac{-5-\sqrt{41}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{41}}{2*1}=\frac{-5+\sqrt{41}}{2}
$