-7x(8-2x)=-4(x+5)

Solution for -7x(8-2x)=-4(x+5) equation:

-7x(8-2x)=-4(x+5)

We move all terms to the left:

-7x(8-2x)-(-4(x+5))=0

We add all the numbers together, and all the variables

-7x(-2x+8)-(-4(x+5))=0

We multiply parentheses

14x^2-56x-(-4(x+5))=0


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

-4(x+5)

We multiply parentheses

-4x-20

Back to the equation:

-(-4x-20)


We get rid of parentheses

14x^2-56x+4x+20=0

We add all the numbers together, and all the variables

14x^2-52x+20=0

a = 14; b = -52; c = +20;
Δ = b2-4ac
Δ = -522-4·14·20
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-52)-12\sqrt{11}}{2*14}=\frac{52-12\sqrt{11}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-52)+12\sqrt{11}}{2*14}=\frac{52+12\sqrt{11}}{28}
$