29=13x+4x^2

Solution for 29=13x+4x^2 equation:

29=13x+4x^2

We move all terms to the left:

29-(13x+4x^2)=0

We get rid of parentheses

-4x^2-13x+29=0

a = -4; b = -13; c = +29;
Δ = b2-4ac
Δ = -132-4·(-4)·29
Δ = 633
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{-(-13)-\sqrt{633}}{2*-4}=\frac{13-\sqrt{633}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{633}}{2*-4}=\frac{13+\sqrt{633}}{-8}
$