13x+2x(x+1)=10

Solution for 13x+2x(x+1)=10 equation:

13x+2x(x+1)=10

We move all terms to the left:

13x+2x(x+1)-(10)=0

We multiply parentheses

2x^2+13x+2x-10=0

We add all the numbers together, and all the variables

2x^2+15x-10=0

a = 2; b = 15; c = -10;
Δ = b2-4ac
Δ = 152-4·2·(-10)
Δ = 305
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{-(15)-\sqrt{305}}{2*2}=\frac{-15-\sqrt{305}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{305}}{2*2}=\frac{-15+\sqrt{305}}{4}
$