3/2x+5=x-14

Solution for 3/2x+5=x-14 equation:

3/2x+5=x-14

We move all terms to the left:

3/2x+5-(x-14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-x+14+5=0

We multiply all the terms by the denominator


-x*2x+14*2x+5*2x+3=0

Wy multiply elements

-2x^2+28x+10x+3=0

We add all the numbers together, and all the variables

-2x^2+38x+3=0

a = -2; b = 38; c = +3;
Δ = b2-4ac
Δ = 382-4·(-2)·3
Δ = 1468
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:

$\sqrt{\Delta}=\sqrt{1468}=\sqrt{4*367}=\sqrt{4}*\sqrt{367}=2\sqrt{367}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{367}}{2*-2}=\frac{-38-2\sqrt{367}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{367}}{2*-2}=\frac{-38+2\sqrt{367}}{-4}
$