-7/8x-5/24x+1/3=-51

Solution for -7/8x-5/24x+1/3=-51 equation:

-7/8x-5/24x+1/3=-51

We move all terms to the left:

-7/8x-5/24x+1/3-(-51)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 24x!=0

x!=0/24

x!=0

x∈R


We add all the numbers together, and all the variables

-7/8x-5/24x+51+1/3=0

We calculate fractions


384x^2/1728x^2+(-1512x)/1728x^2+(-360x)/1728x^2+51=0

We multiply all the terms by the denominator


384x^2+(-1512x)+(-360x)+51*1728x^2=0

Wy multiply elements

384x^2+88128x^2+(-1512x)+(-360x)=0

We get rid of parentheses

384x^2+88128x^2-1512x-360x=0

We add all the numbers together, and all the variables

88512x^2-1872x=0

a = 88512; b = -1872; c = 0;
Δ = b2-4ac
Δ = -18722-4·88512·0
Δ = 3504384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3504384}=1872$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1872)-1872}{2*88512}=\frac{0}{177024}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1872)+1872}{2*88512}=\frac{3744}{177024}
=39/1844
$