3/2x-14=x+13

Solution for 3/2x-14=x+13 equation:

3/2x-14=x+13

We move all terms to the left:

3/2x-14-(x+13)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-x-13-14=0

We multiply all the terms by the denominator


-x*2x-13*2x-14*2x+3=0

Wy multiply elements

-2x^2-26x-28x+3=0

We add all the numbers together, and all the variables

-2x^2-54x+3=0

a = -2; b = -54; c = +3;
Δ = b2-4ac
Δ = -542-4·(-2)·3
Δ = 2940
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:

$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-14\sqrt{15}}{2*-2}=\frac{54-14\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+14\sqrt{15}}{2*-2}=\frac{54+14\sqrt{15}}{-4}
$