5x+8x=13x^2

Solution for 5x+8x=13x^2 equation:

5x+8x=13x^2

We move all terms to the left:

5x+8x-(13x^2)=0

determiningTheFunctionDomain
-13x^2+5x+8x=0

We add all the numbers together, and all the variables

-13x^2+13x=0

a = -13; b = 13; c = 0;
Δ = b2-4ac
Δ = 132-4·(-13)·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-13}{2*-13}=\frac{-26}{-26}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+13}{2*-13}=\frac{0}{-26}
=0
$