x+4/5x-95=1705

Solution for x+4/5x-95=1705 equation:

x+4/5x-95=1705

We move all terms to the left:

x+4/5x-95-(1705)=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-1800=0

We multiply all the terms by the denominator


x*5x-1800*5x+4=0

Wy multiply elements

5x^2-9000x+4=0

a = 5; b = -9000; c = +4;
Δ = b2-4ac
Δ = -90002-4·5·4
Δ = 80999920
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:

$\sqrt{\Delta}=\sqrt{80999920}=\sqrt{274576*295}=\sqrt{274576}*\sqrt{295}=524\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9000)-524\sqrt{295}}{2*5}=\frac{9000-524\sqrt{295}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9000)+524\sqrt{295}}{2*5}=\frac{9000+524\sqrt{295}}{10}
$