25+x=1/2x-3

Solution for 25+x=1/2x-3 equation:

25+x=1/2x-3

We move all terms to the left:

25+x-(1/2x-3)=0


Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

x-1/2x+3+25=0

We multiply all the terms by the denominator


x*2x+3*2x+25*2x-1=0

Wy multiply elements

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

We add all the numbers together, and all the variables

2x^2+56x-1=0

a = 2; b = 56; c = -1;
Δ = b2-4ac
Δ = 562-4·2·(-1)
Δ = 3144
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:

$\sqrt{\Delta}=\sqrt{3144}=\sqrt{4*786}=\sqrt{4}*\sqrt{786}=2\sqrt{786}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-2\sqrt{786}}{2*2}=\frac{-56-2\sqrt{786}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+2\sqrt{786}}{2*2}=\frac{-56+2\sqrt{786}}{4}
$