1/7x+3/8x=5

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

1/7x+3/8x=5

We move all terms to the left:

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


8x/56x^2+21x/56x^2-5=0

We multiply all the terms by the denominator


8x+21x-5*56x^2=0

We add all the numbers together, and all the variables

29x-5*56x^2=0

Wy multiply elements

-280x^2+29x=0

a = -280; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-280)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-280}=\frac{-58}{-560}
=29/280
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-280}=\frac{0}{-560}
=0
$