5/7x+1/6x=407

Solution for 5/7x+1/6x=407 equation:

5/7x+1/6x=407

We move all terms to the left:

5/7x+1/6x-(407)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We calculate fractions


30x/42x^2+7x/42x^2-407=0

We multiply all the terms by the denominator


30x+7x-407*42x^2=0

We add all the numbers together, and all the variables

37x-407*42x^2=0

Wy multiply elements

-17094x^2+37x=0

a = -17094; b = 37; c = 0;
Δ = b2-4ac
Δ = 372-4·(-17094)·0
Δ = 1369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1369}=37$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(37)-37}{2*-17094}=\frac{-74}{-34188}
=1/462
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+37}{2*-17094}=\frac{0}{-34188}
=0
$