3x^2-5x-11/12=0

Solution for 3x^2-5x-11/12=0 equation:

3x^2-5x-11/12=0

We multiply all the terms by the denominator


3x^2*12-5x*12-11=0

Wy multiply elements

36x^2-60x-11=0

a = 36; b = -60; c = -11;
Δ = b2-4ac
Δ = -602-4·36·(-11)
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-72}{2*36}=\frac{-12}{72}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+72}{2*36}=\frac{132}{72}
=1+5/6
$