4/7x+13=6x

Solution for 4/7x+13=6x equation:

4/7x+13=6x

We move all terms to the left:

4/7x+13-(6x)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We add all the numbers together, and all the variables

-6x+4/7x+13=0

We multiply all the terms by the denominator


-6x*7x+13*7x+4=0

Wy multiply elements

-42x^2+91x+4=0

a = -42; b = 91; c = +4;
Δ = b2-4ac
Δ = 912-4·(-42)·4
Δ = 8953
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{-(91)-\sqrt{8953}}{2*-42}=\frac{-91-\sqrt{8953}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+\sqrt{8953}}{2*-42}=\frac{-91+\sqrt{8953}}{-84}
$