140=10x(8+x)

Solution for 140=10x(8+x) equation:

140=10x(8+x)

We move all terms to the left:

140-(10x(8+x))=0

We add all the numbers together, and all the variables

-(10x(x+8))+140=0


We calculate terms in parentheses: -(10x(x+8)), so:

10x(x+8)

We multiply parentheses

10x^2+80x

Back to the equation:

-(10x^2+80x)


We get rid of parentheses

-10x^2-80x+140=0

a = -10; b = -80; c = +140;
Δ = b2-4ac
Δ = -802-4·(-10)·140
Δ = 12000
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:

$\sqrt{\Delta}=\sqrt{12000}=\sqrt{400*30}=\sqrt{400}*\sqrt{30}=20\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-20\sqrt{30}}{2*-10}=\frac{80-20\sqrt{30}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+20\sqrt{30}}{2*-10}=\frac{80+20\sqrt{30}}{-20}
$