5x^2-2x-19=-3

Solution for 5x^2-2x-19=-3 equation:

5x^2-2x-19=-3

We move all terms to the left:

5x^2-2x-19-(-3)=0

We add all the numbers together, and all the variables

5x^2-2x-16=0

a = 5; b = -2; c = -16;
Δ = b2-4ac
Δ = -22-4·5·(-16)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-18}{2*5}=\frac{-16}{10}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+18}{2*5}=\frac{20}{10}
=2
$