54x^2+51x-14=0

Solution for 54x^2+51x-14=0 equation:

54x^2+51x-14=0

a = 54; b = 51; c = -14;
Δ = b2-4ac
Δ = 512-4·54·(-14)
Δ = 5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5625}=75$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-75}{2*54}=\frac{-126}{108}
=-1+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+75}{2*54}=\frac{24}{108}
=2/9
$