1/8x+1/7x=224,000

Solution for 1/8x+1/7x=224,000 equation:

1/8x+1/7x=224.000

We move all terms to the left:

1/8x+1/7x-(224.000)=0


Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

1/8x+1/7x-224=0

We calculate fractions


7x/56x^2+8x/56x^2-224=0

We multiply all the terms by the denominator


7x+8x-224*56x^2=0

We add all the numbers together, and all the variables

15x-224*56x^2=0

Wy multiply elements

-12544x^2+15x=0

a = -12544; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-12544)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-15}{2*-12544}=\frac{-30}{-25088}
=15/12544
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-12544}=\frac{0}{-25088}
=0
$