x^2-3x+9/4-9/4-40=0

Solution for x^2-3x+9/4-9/4-40=0 equation:

x^2-3x+9/4-9/4-40=0

We multiply all the terms by the denominator


x^2*4-3x*4+9-9-40*4=0

We add all the numbers together, and all the variables

x^2*4-3x*4-160=0

Wy multiply elements

4x^2-12x-160=0

a = 4; b = -12; c = -160;
Δ = b2-4ac
Δ = -122-4·4·(-160)
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-52}{2*4}=\frac{-40}{8}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+52}{2*4}=\frac{64}{8}
=8
$