13=29x-5x^2

Solution for 13=29x-5x^2 equation:

13=29x-5x^2

We move all terms to the left:

13-(29x-5x^2)=0

We get rid of parentheses

5x^2-29x+13=0

a = 5; b = -29; c = +13;
Δ = b2-4ac
Δ = -292-4·5·13
Δ = 581
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{-(-29)-\sqrt{581}}{2*5}=\frac{29-\sqrt{581}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{581}}{2*5}=\frac{29+\sqrt{581}}{10}
$