1/5x=6+7x

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

1/5x=6+7x

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

1/5x-7x-6=0

We multiply all the terms by the denominator


-7x*5x-6*5x+1=0

Wy multiply elements

-35x^2-30x+1=0

a = -35; b = -30; c = +1;
Δ = b2-4ac
Δ = -302-4·(-35)·1
Δ = 1040
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-4\sqrt{65}}{2*-35}=\frac{30-4\sqrt{65}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+4\sqrt{65}}{2*-35}=\frac{30+4\sqrt{65}}{-70}
$