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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

5(x+4)-(7(-1x+8)x)=0

We multiply parentheses

5x-(7(-1x+8)x)+20=0


We calculate terms in parentheses: -(7(-1x+8)x), so:

7(-1x+8)x

We multiply parentheses

-7x^2+56x

Back to the equation:

-(-7x^2+56x)


We get rid of parentheses

7x^2-56x+5x+20=0

We add all the numbers together, and all the variables

7x^2-51x+20=0

a = 7; b = -51; c = +20;
Δ = b2-4ac
Δ = -512-4·7·20
Δ = 2041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-51)-\sqrt{2041}}{2*7}=\frac{51-\sqrt{2041}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-51)+\sqrt{2041}}{2*7}=\frac{51+\sqrt{2041}}{14}
$