4/5x+x=37

Solution for 4/5x+x=37 equation:

4/5x+x=37

We move all terms to the left:

4/5x+x-(37)=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+4/5x-37=0

We multiply all the terms by the denominator


x*5x-37*5x+4=0

Wy multiply elements

5x^2-185x+4=0

a = 5; b = -185; c = +4;
Δ = b2-4ac
Δ = -1852-4·5·4
Δ = 34145
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-185)-\sqrt{34145}}{2*5}=\frac{185-\sqrt{34145}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-185)+\sqrt{34145}}{2*5}=\frac{185+\sqrt{34145}}{10}
$