3x+x(x+2)=10

Solution for 3x+x(x+2)=10 equation:

3x+x(x+2)=10

We move all terms to the left:

3x+x(x+2)-(10)=0

We multiply parentheses

x^2+3x+2x-10=0

We add all the numbers together, and all the variables

x^2+5x-10=0

a = 1; b = 5; c = -10;
Δ = b2-4ac
Δ = 52-4·1·(-10)
Δ = 65
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{-(5)-\sqrt{65}}{2*1}=\frac{-5-\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{65}}{2*1}=\frac{-5+\sqrt{65}}{2}
$