x+5/7x=60

Solution for x+5/7x=60 equation:

x+5/7x=60

We move all terms to the left:

x+5/7x-(60)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We multiply all the terms by the denominator


x*7x-60*7x+5=0

Wy multiply elements

7x^2-420x+5=0

a = 7; b = -420; c = +5;
Δ = b2-4ac
Δ = -4202-4·7·5
Δ = 176260
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:

$\sqrt{\Delta}=\sqrt{176260}=\sqrt{4*44065}=\sqrt{4}*\sqrt{44065}=2\sqrt{44065}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-420)-2\sqrt{44065}}{2*7}=\frac{420-2\sqrt{44065}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-420)+2\sqrt{44065}}{2*7}=\frac{420+2\sqrt{44065}}{14}
$