1/2x+10+3/2x=X+1

Solution for 1/2x+10+3/2x=X+1 equation:

1/2x+10+3/2x=x+1

We move all terms to the left:

1/2x+10+3/2x-(x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+3/2x-x-1+10=0

We multiply all the terms by the denominator


-x*2x-1*2x+10*2x+1+3=0

We add all the numbers together, and all the variables

-x*2x-1*2x+10*2x+4=0

Wy multiply elements

-2x^2-2x+20x+4=0

We add all the numbers together, and all the variables

-2x^2+18x+4=0

a = -2; b = 18; c = +4;
Δ = b2-4ac
Δ = 182-4·(-2)·4
Δ = 356
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:

$\sqrt{\Delta}=\sqrt{356}=\sqrt{4*89}=\sqrt{4}*\sqrt{89}=2\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{89}}{2*-2}=\frac{-18-2\sqrt{89}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{89}}{2*-2}=\frac{-18+2\sqrt{89}}{-4}
$