4/5x+x=252

Solution for 4/5x+x=252 equation:

4/5x+x=252

We move all terms to the left:

4/5x+x-(252)=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-252=0

We multiply all the terms by the denominator


x*5x-252*5x+4=0

Wy multiply elements

5x^2-1260x+4=0

a = 5; b = -1260; c = +4;
Δ = b2-4ac
Δ = -12602-4·5·4
Δ = 1587520
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:

$\sqrt{\Delta}=\sqrt{1587520}=\sqrt{7744*205}=\sqrt{7744}*\sqrt{205}=88\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1260)-88\sqrt{205}}{2*5}=\frac{1260-88\sqrt{205}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1260)+88\sqrt{205}}{2*5}=\frac{1260+88\sqrt{205}}{10}
$