4x2-13x+13=4x+9

Solution for 4x2-13x+13=4x+9 equation:

4x^2-13x+13=4x+9

We move all terms to the left:

4x^2-13x+13-(4x+9)=0

We get rid of parentheses

4x^2-13x-4x-9+13=0

We add all the numbers together, and all the variables

4x^2-17x+4=0

a = 4; b = -17; c = +4;
Δ = b2-4ac
Δ = -172-4·4·4
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-15}{2*4}=\frac{2}{8}
=1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+15}{2*4}=\frac{32}{8}
=4
$