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

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

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

We multiply all the terms by the denominator


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

Wy multiply elements

4x^2+12x-3=0

a = 4; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·4·(-3)
Δ = 192
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{192}=\sqrt{64*3}=\sqrt{64}*\sqrt{3}=8\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{3}}{2*4}=\frac{-12-8\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{3}}{2*4}=\frac{-12+8\sqrt{3}}{8}
$