10x(8+x)=190

Solution for 10x(8+x)=190 equation:

10x(8+x)=190

We move all terms to the left:

10x(8+x)-(190)=0

We add all the numbers together, and all the variables

10x(x+8)-190=0

We multiply parentheses

10x^2+80x-190=0

a = 10; b = 80; c = -190;
Δ = b2-4ac
Δ = 802-4·10·(-190)
Δ = 14000
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:

$\sqrt{\Delta}=\sqrt{14000}=\sqrt{400*35}=\sqrt{400}*\sqrt{35}=20\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-20\sqrt{35}}{2*10}=\frac{-80-20\sqrt{35}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+20\sqrt{35}}{2*10}=\frac{-80+20\sqrt{35}}{20}
$