47=4/5x+7x=

Solution for 47=4/5x+7x= equation:

47=4/5x+7x=

We move all terms to the left:

47-(4/5x+7x)=0


Domain of the equation: 5x+7x)!=0

x∈R


We add all the numbers together, and all the variables

-(+7x+4/5x)+47=0

We get rid of parentheses

-7x-4/5x+47=0

We multiply all the terms by the denominator


-7x*5x+47*5x-4=0

Wy multiply elements

-35x^2+235x-4=0

a = -35; b = 235; c = -4;
Δ = b2-4ac
Δ = 2352-4·(-35)·(-4)
Δ = 54665
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:

$\sqrt{\Delta}=\sqrt{54665}=\sqrt{841*65}=\sqrt{841}*\sqrt{65}=29\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(235)-29\sqrt{65}}{2*-35}=\frac{-235-29\sqrt{65}}{-70}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(235)+29\sqrt{65}}{2*-35}=\frac{-235+29\sqrt{65}}{-70}
$