8x-4/6x+18=0

Solution for 8x-4/6x+18=0 equation:

8x-4/6x+18=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


8x*6x+18*6x-4=0

Wy multiply elements

48x^2+108x-4=0

a = 48; b = 108; c = -4;
Δ = b2-4ac
Δ = 1082-4·48·(-4)
Δ = 12432
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:

$\sqrt{\Delta}=\sqrt{12432}=\sqrt{16*777}=\sqrt{16}*\sqrt{777}=4\sqrt{777}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-4\sqrt{777}}{2*48}=\frac{-108-4\sqrt{777}}{96}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+4\sqrt{777}}{2*48}=\frac{-108+4\sqrt{777}}{96}
$