2(x-3)-5=4x(x-5)

Solution for 2(x-3)-5=4x(x-5) equation:

2(x-3)-5=4x(x-5)

We move all terms to the left:

2(x-3)-5-(4x(x-5))=0

We multiply parentheses

2x-(4x(x-5))-6-5=0


We calculate terms in parentheses: -(4x(x-5)), so:

4x(x-5)

We multiply parentheses

4x^2-20x

Back to the equation:

-(4x^2-20x)


We add all the numbers together, and all the variables

2x-(4x^2-20x)-11=0

We get rid of parentheses

-4x^2+2x+20x-11=0

We add all the numbers together, and all the variables

-4x^2+22x-11=0

a = -4; b = 22; c = -11;
Δ = b2-4ac
Δ = 222-4·(-4)·(-11)
Δ = 308
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:

$\sqrt{\Delta}=\sqrt{308}=\sqrt{4*77}=\sqrt{4}*\sqrt{77}=2\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{77}}{2*-4}=\frac{-22-2\sqrt{77}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{77}}{2*-4}=\frac{-22+2\sqrt{77}}{-8}
$