-5/6x-1/8x=-102

Solution for -5/6x-1/8x=-102 equation:

-5/6x-1/8x=-102

We move all terms to the left:

-5/6x-1/8x-(-102)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

-5/6x-1/8x+102=0

We calculate fractions


(-40x)/48x^2+(-6x)/48x^2+102=0

We multiply all the terms by the denominator


(-40x)+(-6x)+102*48x^2=0

Wy multiply elements

4896x^2+(-40x)+(-6x)=0

We get rid of parentheses

4896x^2-40x-6x=0

We add all the numbers together, and all the variables

4896x^2-46x=0

a = 4896; b = -46; c = 0;
Δ = b2-4ac
Δ = -462-4·4896·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-46}{2*4896}=\frac{0}{9792}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+46}{2*4896}=\frac{92}{9792}
=23/2448
$