7/5x+x=72

Solution for 7/5x+x=72 equation:

7/5x+x=72

We move all terms to the left:

7/5x+x-(72)=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-72=0

We multiply all the terms by the denominator


x*5x-72*5x+7=0

Wy multiply elements

5x^2-360x+7=0

a = 5; b = -360; c = +7;
Δ = b2-4ac
Δ = -3602-4·5·7
Δ = 129460
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:

$\sqrt{\Delta}=\sqrt{129460}=\sqrt{4*32365}=\sqrt{4}*\sqrt{32365}=2\sqrt{32365}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-360)-2\sqrt{32365}}{2*5}=\frac{360-2\sqrt{32365}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-360)+2\sqrt{32365}}{2*5}=\frac{360+2\sqrt{32365}}{10}
$