4/5x+x=126

Solution for 4/5x+x=126 equation:

4/5x+x=126

We move all terms to the left:

4/5x+x-(126)=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-126=0

We multiply all the terms by the denominator


x*5x-126*5x+4=0

Wy multiply elements

5x^2-630x+4=0

a = 5; b = -630; c = +4;
Δ = b2-4ac
Δ = -6302-4·5·4
Δ = 396820
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:

$\sqrt{\Delta}=\sqrt{396820}=\sqrt{4*99205}=\sqrt{4}*\sqrt{99205}=2\sqrt{99205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-630)-2\sqrt{99205}}{2*5}=\frac{630-2\sqrt{99205}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-630)+2\sqrt{99205}}{2*5}=\frac{630+2\sqrt{99205}}{10}
$