54x*x-10x-5=0

Solution for 54x*x-10x-5=0 equation:

54x*x-10x-5=0

We add all the numbers together, and all the variables

-10x+54x*x-5=0

Wy multiply elements

54x^2-10x-5=0

a = 54; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·54·(-5)
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{295}}{2*54}=\frac{10-2\sqrt{295}}{108}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{295}}{2*54}=\frac{10+2\sqrt{295}}{108}
$