4/5x+x=124

Solution for 4/5x+x=124 equation:

4/5x+x=124

We move all terms to the left:

4/5x+x-(124)=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-124=0

We multiply all the terms by the denominator


x*5x-124*5x+4=0

Wy multiply elements

5x^2-620x+4=0

a = 5; b = -620; c = +4;
Δ = b2-4ac
Δ = -6202-4·5·4
Δ = 384320
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:

$\sqrt{\Delta}=\sqrt{384320}=\sqrt{64*6005}=\sqrt{64}*\sqrt{6005}=8\sqrt{6005}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-620)-8\sqrt{6005}}{2*5}=\frac{620-8\sqrt{6005}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-620)+8\sqrt{6005}}{2*5}=\frac{620+8\sqrt{6005}}{10}
$