5x2-4x-9=3

Solution for 5x2-4x-9=3 equation:

5x^2-4x-9=3

We move all terms to the left:

5x^2-4x-9-(3)=0

We add all the numbers together, and all the variables

5x^2-4x-12=0

a = 5; b = -4; c = -12;
Δ = b2-4ac
Δ = -42-4·5·(-12)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-16}{2*5}=\frac{-12}{10}
=-1+1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+16}{2*5}=\frac{20}{10}
=2
$