13-13x=4x^2+12x-16=0

Solution for 13-13x=4x^2+12x-16=0 equation:

13-13x=4x^2+12x-16=0

We move all terms to the left:

13-13x-(4x^2+12x-16)=0

We get rid of parentheses

-4x^2-13x-12x+16+13=0

We add all the numbers together, and all the variables

-4x^2-25x+29=0

a = -4; b = -25; c = +29;
Δ = b2-4ac
Δ = -252-4·(-4)·29
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-33}{2*-4}=\frac{-8}{-8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+33}{2*-4}=\frac{58}{-8}
=-7+1/4
$