X=7/5y+2000

Solution for X=7/5y+2000 equation:

X=7/5X+2000

We move all terms to the left:

X-(7/5X+2000)=0


Domain of the equation: 5X+2000)!=0

X∈R


We get rid of parentheses

X-7/5X-2000=0

We multiply all the terms by the denominator


X*5X-2000*5X-7=0

Wy multiply elements

5X^2-10000X-7=0

a = 5; b = -10000; c = -7;
Δ = b2-4ac
Δ = -100002-4·5·(-7)
Δ = 100000140
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:

$\sqrt{\Delta}=\sqrt{100000140}=\sqrt{4*25000035}=\sqrt{4}*\sqrt{25000035}=2\sqrt{25000035}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10000)-2\sqrt{25000035}}{2*5}=\frac{10000-2\sqrt{25000035}}{10}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10000)+2\sqrt{25000035}}{2*5}=\frac{10000+2\sqrt{25000035}}{10}
$