3/2x-14=2x+13

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

3/2x-14=2x+13

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2-26x-28x+3=0

We add all the numbers together, and all the variables

-4x^2-54x+3=0

a = -4; b = -54; c = +3;
Δ = b2-4ac
Δ = -542-4·(-4)·3
Δ = 2964
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:

$\sqrt{\Delta}=\sqrt{2964}=\sqrt{4*741}=\sqrt{4}*\sqrt{741}=2\sqrt{741}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{741}}{2*-4}=\frac{54-2\sqrt{741}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{741}}{2*-4}=\frac{54+2\sqrt{741}}{-8}
$