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

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

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+16x-9=0

a = 4; b = 16; c = -9;
Δ = b2-4ac
Δ = 162-4·4·(-9)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-20}{2*4}=\frac{-36}{8}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+20}{2*4}=\frac{4}{8}
=1/2
$