4/7x+1/8x=120

Solution for 4/7x+1/8x=120 equation:

4/7x+1/8x=120

We move all terms to the left:

4/7x+1/8x-(120)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We calculate fractions


32x/56x^2+7x/56x^2-120=0

We multiply all the terms by the denominator


32x+7x-120*56x^2=0

We add all the numbers together, and all the variables

39x-120*56x^2=0

Wy multiply elements

-6720x^2+39x=0

a = -6720; b = 39; c = 0;
Δ = b2-4ac
Δ = 392-4·(-6720)·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-39}{2*-6720}=\frac{-78}{-13440}
=13/2240
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+39}{2*-6720}=\frac{0}{-13440}
=0
$