X+11/5x*7=470

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

X+11/5X*7=470

We move all terms to the left:

X+11/5X*7-(470)=0


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

X!=0/1

X!=0

X∈R


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}
$