11/5x*7+x=470

Solution for 11/5x*7+x=470 equation:

11/5x*7+x=470

We move all terms to the left:

11/5x*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+11/5x*7-470=0

We multiply all the terms by the denominator


x*5x*7-470*5x*7+11=0

Wy multiply elements

35x^2*7-16450x*7+11=0

Wy multiply elements

245x^2-115150x+11=0

a = 245; b = -115150; c = +11;
Δ = b2-4ac
Δ = -1151502-4·245·11
Δ = 13259511720
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:

$\sqrt{\Delta}=\sqrt{13259511720}=\sqrt{1764*7516730}=\sqrt{1764}*\sqrt{7516730}=42\sqrt{7516730}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-115150)-42\sqrt{7516730}}{2*245}=\frac{115150-42\sqrt{7516730}}{490}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-115150)+42\sqrt{7516730}}{2*245}=\frac{115150+42\sqrt{7516730}}{490}
$