850=5x+x(x+10)

Solution for 850=5x+x(x+10) equation:

850=5x+x(x+10)

We move all terms to the left:

850-(5x+x(x+10))=0


We calculate terms in parentheses: -(5x+x(x+10)), so:

5x+x(x+10)

We multiply parentheses

x^2+5x+10x

We add all the numbers together, and all the variables

x^2+15x

Back to the equation:

-(x^2+15x)


We get rid of parentheses

-x^2-15x+850=0

We add all the numbers together, and all the variables

-1x^2-15x+850=0

a = -1; b = -15; c = +850;
Δ = b2-4ac
Δ = -152-4·(-1)·850
Δ = 3625
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:

$\sqrt{\Delta}=\sqrt{3625}=\sqrt{25*145}=\sqrt{25}*\sqrt{145}=5\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-5\sqrt{145}}{2*-1}=\frac{15-5\sqrt{145}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+5\sqrt{145}}{2*-1}=\frac{15+5\sqrt{145}}{-2}
$