54x2+51x+7=0

Solution for 54x2+51x+7=0 equation:

54x^2+51x+7=0

a = 54; b = 51; c = +7;
Δ = b2-4ac
Δ = 512-4·54·7
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-33}{2*54}=\frac{-84}{108}
=-7/9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+33}{2*54}=\frac{-18}{108}
=-1/6
$