1/7x=-1/8x+30

Solution for 1/7x=-1/8x+30 equation:

1/7x=-1/8x+30

We move all terms to the left:

1/7x-(-1/8x+30)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 8x+30)!=0

x∈R


We get rid of parentheses

1/7x+1/8x-30=0

We calculate fractions


8x/56x^2+7x/56x^2-30=0

We multiply all the terms by the denominator


8x+7x-30*56x^2=0

We add all the numbers together, and all the variables

15x-30*56x^2=0

Wy multiply elements

-1680x^2+15x=0

a = -1680; b = 15; c = 0;
Δ = b2-4ac
Δ = 152-4·(-1680)·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*-1680}=\frac{-30}{-3360}
=1/112
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+15}{2*-1680}=\frac{0}{-3360}
=0
$