4(x-5)-3x=2x(x-10)-x

Solution for 4(x-5)-3x=2x(x-10)-x equation:

4(x-5)-3x=2x(x-10)-x

We move all terms to the left:

4(x-5)-3x-(2x(x-10)-x)=0

We add all the numbers together, and all the variables

-3x+4(x-5)-(2x(x-10)-x)=0

We multiply parentheses

-3x+4x-(2x(x-10)-x)-20=0


We calculate terms in parentheses: -(2x(x-10)-x), so:

2x(x-10)-x

We add all the numbers together, and all the variables

-1x+2x(x-10)

We multiply parentheses

2x^2-1x-20x

We add all the numbers together, and all the variables

2x^2-21x

Back to the equation:

-(2x^2-21x)


We add all the numbers together, and all the variables

x-(2x^2-21x)-20=0

We get rid of parentheses

-2x^2+x+21x-20=0

We add all the numbers together, and all the variables

-2x^2+22x-20=0

a = -2; b = 22; c = -20;
Δ = b2-4ac
Δ = 222-4·(-2)·(-20)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-18}{2*-2}=\frac{-40}{-4}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+18}{2*-2}=\frac{-4}{-4}
=1
$