x^2+9x+13=5x^2

Solution for x^2+9x+13=5x^2 equation:

x^2+9x+13=5x^2

We move all terms to the left:

x^2+9x+13-(5x^2)=0

determiningTheFunctionDomain
x^2-5x^2+9x+13=0

We add all the numbers together, and all the variables

-4x^2+9x+13=0

a = -4; b = 9; c = +13;
Δ = b2-4ac
Δ = 92-4·(-4)·13
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-17}{2*-4}=\frac{-26}{-8}
=3+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+17}{2*-4}=\frac{8}{-8}
=-1
$