10x-(x-16)=2x(5+x)

Solution for 10x-(x-16)=2x(5+x) equation:

10x-(x-16)=2x(5+x)

We move all terms to the left:

10x-(x-16)-(2x(5+x))=0

We add all the numbers together, and all the variables

10x-(x-16)-(2x(x+5))=0

We get rid of parentheses

10x-x-(2x(x+5))+16=0


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

2x(x+5)

We multiply parentheses

2x^2+10x

Back to the equation:

-(2x^2+10x)


We add all the numbers together, and all the variables

9x-(2x^2+10x)+16=0

We get rid of parentheses

-2x^2+9x-10x+16=0

We add all the numbers together, and all the variables

-2x^2-1x+16=0

a = -2; b = -1; c = +16;
Δ = b2-4ac
Δ = -12-4·(-2)·16
Δ = 129
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{-(-1)-\sqrt{129}}{2*-2}=\frac{1-\sqrt{129}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{129}}{2*-2}=\frac{1+\sqrt{129}}{-4}
$