3/2x+5=25+x

Solution for 3/2x+5=25+x equation:

3/2x+5=25+x

We move all terms to the left:

3/2x+5-(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

3/2x-(x+25)+5=0

We get rid of parentheses

3/2x-x-25+5=0

We multiply all the terms by the denominator


-x*2x-25*2x+5*2x+3=0

Wy multiply elements

-2x^2-50x+10x+3=0

We add all the numbers together, and all the variables

-2x^2-40x+3=0

a = -2; b = -40; c = +3;
Δ = b2-4ac
Δ = -402-4·(-2)·3
Δ = 1624
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:

$\sqrt{\Delta}=\sqrt{1624}=\sqrt{4*406}=\sqrt{4}*\sqrt{406}=2\sqrt{406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{406}}{2*-2}=\frac{40-2\sqrt{406}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{406}}{2*-2}=\frac{40+2\sqrt{406}}{-4}
$