8=5*(3/5x)-x(x-7)

Solution for 8=5*(3/5x)-x(x-7) equation:

8=5(3/5x)-x(x-7)

We move all terms to the left:

8-(5(3/5x)-x(x-7))=0


Domain of the equation: 5x)-x(x-7))!=0

x∈R


We add all the numbers together, and all the variables

-(5(+3/5x)-x(x-7))+8=0

We multiply all the terms by the denominator


-(5(+3+8*5x)-x(x-7))=0


We calculate terms in parentheses: -(5(+3+8*5x)-x(x-7)), so:

5(+3+8*5x)-x(x-7)

We add all the numbers together, and all the variables

5(8*5x+3)-x(x-7)

We multiply parentheses

-x^2+200x+7x+15

We add all the numbers together, and all the variables

-1x^2+207x+15

Back to the equation:

-(-1x^2+207x+15)


We get rid of parentheses

1x^2-207x-15=0

We add all the numbers together, and all the variables

x^2-207x-15=0

a = 1; b = -207; c = -15;
Δ = b2-4ac
Δ = -2072-4·1·(-15)
Δ = 42909
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{-(-207)-\sqrt{42909}}{2*1}=\frac{207-\sqrt{42909}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-207)+\sqrt{42909}}{2*1}=\frac{207+\sqrt{42909}}{2}
$