25x=1/2x-20

Solution for 25x=1/2x-20 equation:

25x=1/2x-20

We move all terms to the left:

25x-(1/2x-20)=0


Domain of the equation: 2x-20)!=0

x∈R


We get rid of parentheses

25x-1/2x+20=0

We multiply all the terms by the denominator


25x*2x+20*2x-1=0

Wy multiply elements

50x^2+40x-1=0

a = 50; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·50·(-1)
Δ = 1800
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:

$\sqrt{\Delta}=\sqrt{1800}=\sqrt{900*2}=\sqrt{900}*\sqrt{2}=30\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-30\sqrt{2}}{2*50}=\frac{-40-30\sqrt{2}}{100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+30\sqrt{2}}{2*50}=\frac{-40+30\sqrt{2}}{100}
$