4x^2-13x=-9

Solution for 4x^2-13x=-9 equation:

4x^2-13x=-9

We move all terms to the left:

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

We add all the numbers together, and all the variables

4x^2-13x+9=0

a = 4; b = -13; c = +9;
Δ = b2-4ac
Δ = -132-4·4·9
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-5}{2*4}=\frac{8}{8}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+5}{2*4}=\frac{18}{8}
=2+1/4
$