-4(2x-5)=-6x(2-x)-10x

Solution for -4(2x-5)=-6x(2-x)-10x equation:

-4(2x-5)=-6x(2-x)-10x

We move all terms to the left:

-4(2x-5)-(-6x(2-x)-10x)=0

We add all the numbers together, and all the variables

-4(2x-5)-(-6x(-1x+2)-10x)=0

We multiply parentheses

-8x-(-6x(-1x+2)-10x)+20=0


We calculate terms in parentheses: -(-6x(-1x+2)-10x), so:

-6x(-1x+2)-10x

We add all the numbers together, and all the variables

-10x-6x(-1x+2)

We multiply parentheses

6x^2-10x-12x

We add all the numbers together, and all the variables

6x^2-22x

Back to the equation:

-(6x^2-22x)


We get rid of parentheses

-6x^2-8x+22x+20=0

We add all the numbers together, and all the variables

-6x^2+14x+20=0

a = -6; b = 14; c = +20;
Δ = b2-4ac
Δ = 142-4·(-6)·20
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-26}{2*-6}=\frac{-40}{-12}
=3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+26}{2*-6}=\frac{12}{-12}
=-1
$