7/5x+x=60

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

7/5x+x=60

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

x+7/5x-60=0

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-300x+7=0

a = 5; b = -300; c = +7;
Δ = b2-4ac
Δ = -3002-4·5·7
Δ = 89860
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:

$\sqrt{\Delta}=\sqrt{89860}=\sqrt{4*22465}=\sqrt{4}*\sqrt{22465}=2\sqrt{22465}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-2\sqrt{22465}}{2*5}=\frac{300-2\sqrt{22465}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+2\sqrt{22465}}{2*5}=\frac{300+2\sqrt{22465}}{10}
$