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

Solution for 4(x-5)+2x=-2x(x-6) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x+4x-(-2x(x-6))-20=0


We calculate terms in parentheses: -(-2x(x-6)), so:

-2x(x-6)

We multiply parentheses

-2x^2+12x

Back to the equation:

-(-2x^2+12x)


We add all the numbers together, and all the variables

-(-2x^2+12x)+6x-20=0

We get rid of parentheses

2x^2-12x+6x-20=0

We add all the numbers together, and all the variables

2x^2-6x-20=0

a = 2; b = -6; c = -20;
Δ = b2-4ac
Δ = -62-4·2·(-20)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14}{2*2}=\frac{20}{4}
=5
$