3x+13=2x(x+9)

Solution for 3x+13=2x(x+9) equation:

3x+13=2x(x+9)

We move all terms to the left:

3x+13-(2x(x+9))=0


We calculate terms in parentheses: -(2x(x+9)), so:

2x(x+9)

We multiply parentheses

2x^2+18x

Back to the equation:

-(2x^2+18x)


We get rid of parentheses

-2x^2+3x-18x+13=0

We add all the numbers together, and all the variables

-2x^2-15x+13=0

a = -2; b = -15; c = +13;
Δ = b2-4ac
Δ = -152-4·(-2)·13
Δ = 329
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{329}}{2*-2}=\frac{15-\sqrt{329}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{329}}{2*-2}=\frac{15+\sqrt{329}}{-4}
$