-5/8x-1/9x=-102

Solution for -5/8x-1/9x=-102 equation:

-5/8x-1/9x=-102

We move all terms to the left:

-5/8x-1/9x-(-102)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 9x!=0

x!=0/9

x!=0

x∈R


We add all the numbers together, and all the variables

-5/8x-1/9x+102=0

We calculate fractions


(-45x)/72x^2+(-8x)/72x^2+102=0

We multiply all the terms by the denominator


(-45x)+(-8x)+102*72x^2=0

Wy multiply elements

7344x^2+(-45x)+(-8x)=0

We get rid of parentheses

7344x^2-45x-8x=0

We add all the numbers together, and all the variables

7344x^2-53x=0

a = 7344; b = -53; c = 0;
Δ = b2-4ac
Δ = -532-4·7344·0
Δ = 2809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2809}=53$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-53}{2*7344}=\frac{0}{14688}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+53}{2*7344}=\frac{106}{14688}
=53/7344
$