29x=5x^2-13

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

29x=5x^2-13

We move all terms to the left:

29x-(5x^2-13)=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 = 1101
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{1101}}{2*-5}=\frac{-29-\sqrt{1101}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{1101}}{2*-5}=\frac{-29+\sqrt{1101}}{-10}
$