-7(x-4)2x=-2(x-5)

Solution for -7(x-4)2x=-2(x-5) equation:

-7(x-4)2x=-2(x-5)

We move all terms to the left:

-7(x-4)2x-(-2(x-5))=0

We multiply parentheses

-14x^2+56x-(-2(x-5))=0


We calculate terms in parentheses: -(-2(x-5)), so:

-2(x-5)

We multiply parentheses

-2x+10

Back to the equation:

-(-2x+10)


We get rid of parentheses

-14x^2+56x+2x-10=0

We add all the numbers together, and all the variables

-14x^2+58x-10=0

a = -14; b = 58; c = -10;
Δ = b2-4ac
Δ = 582-4·(-14)·(-10)
Δ = 2804
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:

$\sqrt{\Delta}=\sqrt{2804}=\sqrt{4*701}=\sqrt{4}*\sqrt{701}=2\sqrt{701}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(58)-2\sqrt{701}}{2*-14}=\frac{-58-2\sqrt{701}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(58)+2\sqrt{701}}{2*-14}=\frac{-58+2\sqrt{701}}{-28}
$