2x-5=4(x-2)x

Solution for 2x-5=4(x-2)x equation:

2x-5=4(x-2)x

We move all terms to the left:

2x-5-(4(x-2)x)=0


We calculate terms in parentheses: -(4(x-2)x), so:

4(x-2)x

We multiply parentheses

4x^2-8x

Back to the equation:

-(4x^2-8x)


We get rid of parentheses

-4x^2+2x+8x-5=0

We add all the numbers together, and all the variables

-4x^2+10x-5=0

a = -4; b = 10; c = -5;
Δ = b2-4ac
Δ = 102-4·(-4)·(-5)
Δ = 20
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{5}}{2*-4}=\frac{-10-2\sqrt{5}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{5}}{2*-4}=\frac{-10+2\sqrt{5}}{-8}
$