4x^2-13x=-5

Solution for 4x^2-13x=-5 equation:

4x^2-13x=-5

We move all terms to the left:

4x^2-13x-(-5)=0

We add all the numbers together, and all the variables

4x^2-13x+5=0

a = 4; b = -13; c = +5;
Δ = b2-4ac
Δ = -132-4·4·5
Δ = 89
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{89}}{2*4}=\frac{13-\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{89}}{2*4}=\frac{13+\sqrt{89}}{8}
$