5x-(x+4)=10-2(x-8)5x-x-4=10-2x+164x-4

Solution for 5x-(x+4)=10-2(x-8)5x-x-4=10-2x+164x-4 equation:

5x-(x+4)=10-2(x-8)5x-x-4=10-2x+164x-4

We move all terms to the left:

5x-(x+4)-(10-2(x-8)5x-x-4)=0

We get rid of parentheses

5x-x-(10-2(x-8)5x-x-4)-4=0


We calculate terms in parentheses: -(10-2(x-8)5x-x-4), so:

10-2(x-8)5x-x-4

determiningTheFunctionDomain
-2(x-8)5x-x+10-4

We add all the numbers together, and all the variables

-1x-2(x-8)5x+6

We multiply parentheses

-10x^2-1x+80x+6

We add all the numbers together, and all the variables

-10x^2+79x+6

Back to the equation:

-(-10x^2+79x+6)


We add all the numbers together, and all the variables

-(-10x^2+79x+6)+4x-4=0

We get rid of parentheses

10x^2-79x+4x-6-4=0

We add all the numbers together, and all the variables

10x^2-75x-10=0

a = 10; b = -75; c = -10;
Δ = b2-4ac
Δ = -752-4·10·(-10)
Δ = 6025
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:

$\sqrt{\Delta}=\sqrt{6025}=\sqrt{25*241}=\sqrt{25}*\sqrt{241}=5\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{241}}{2*10}=\frac{75-5\sqrt{241}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{241}}{2*10}=\frac{75+5\sqrt{241}}{20}
$