1/2x-2x=25+x

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

1/2x-2x=25+x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x+1/2x-x-25=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-2x^2-50x+1=0

We add all the numbers together, and all the variables

-6x^2-50x+1=0

a = -6; b = -50; c = +1;
Δ = b2-4ac
Δ = -502-4·(-6)·1
Δ = 2524
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:

$\sqrt{\Delta}=\sqrt{2524}=\sqrt{4*631}=\sqrt{4}*\sqrt{631}=2\sqrt{631}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{631}}{2*-6}=\frac{50-2\sqrt{631}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{631}}{2*-6}=\frac{50+2\sqrt{631}}{-12}
$