6/5x*7+x=470

Solution for 6/5x*7+x=470 equation:

6/5x*7+x=470

We move all terms to the left:

6/5x*7+x-(470)=0


Domain of the equation: 5x*7!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x+6/5x*7-470=0

We multiply all the terms by the denominator


x*5x*7-470*5x*7+6=0

Wy multiply elements

35x^2*7-16450x*7+6=0

Wy multiply elements

245x^2-115150x+6=0

a = 245; b = -115150; c = +6;
Δ = b2-4ac
Δ = -1151502-4·245·6
Δ = 13259516620
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:

$\sqrt{\Delta}=\sqrt{13259516620}=\sqrt{196*67650595}=\sqrt{196}*\sqrt{67650595}=14\sqrt{67650595}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-115150)-14\sqrt{67650595}}{2*245}=\frac{115150-14\sqrt{67650595}}{490}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-115150)+14\sqrt{67650595}}{2*245}=\frac{115150+14\sqrt{67650595}}{490}
$