4x^2-17x+13=-2

Solution for 4x^2-17x+13=-2 equation:

4x^2-17x+13=-2

We move all terms to the left:

4x^2-17x+13-(-2)=0

We add all the numbers together, and all the variables

4x^2-17x+15=0

a = 4; b = -17; c = +15;
Δ = b2-4ac
Δ = -172-4·4·15
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-7}{2*4}=\frac{10}{8}
=1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+7}{2*4}=\frac{24}{8}
=3
$