1/7x+5=3x+4

Solution for 1/7x+5=3x+4 equation:

1/7x+5=3x+4

We move all terms to the left:

1/7x+5-(3x+4)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We get rid of parentheses

1/7x-3x-4+5=0

We multiply all the terms by the denominator


-3x*7x-4*7x+5*7x+1=0

Wy multiply elements

-21x^2-28x+35x+1=0

We add all the numbers together, and all the variables

-21x^2+7x+1=0

a = -21; b = 7; c = +1;
Δ = b2-4ac
Δ = 72-4·(-21)·1
Δ = 133
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{133}}{2*-21}=\frac{-7-\sqrt{133}}{-42}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{133}}{2*-21}=\frac{-7+\sqrt{133}}{-42}
$