9/2x+15=x+20/2

Solution for 9/2x+15=x+20/2 equation:

9/2x+15=x+20/2

We move all terms to the left:

9/2x+15-(x+20/2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

9/2x-(x+10)+15=0

We get rid of parentheses

9/2x-x-10+15=0

We multiply all the terms by the denominator


-x*2x-10*2x+15*2x+9=0

Wy multiply elements

-2x^2-20x+30x+9=0

We add all the numbers together, and all the variables

-2x^2+10x+9=0

a = -2; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·(-2)·9
Δ = 172
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:

$\sqrt{\Delta}=\sqrt{172}=\sqrt{4*43}=\sqrt{4}*\sqrt{43}=2\sqrt{43}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{43}}{2*-2}=\frac{-10-2\sqrt{43}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{43}}{2*-2}=\frac{-10+2\sqrt{43}}{-4}
$