3/2x-13=5x+1

Solution for 3/2x-13=5x+1 equation:

3/2x-13=5x+1

We move all terms to the left:

3/2x-13-(5x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-5x-1-13=0

We multiply all the terms by the denominator


-5x*2x-1*2x-13*2x+3=0

Wy multiply elements

-10x^2-2x-26x+3=0

We add all the numbers together, and all the variables

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

a = -10; b = -28; c = +3;
Δ = b2-4ac
Δ = -282-4·(-10)·3
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{226}}{2*-10}=\frac{28-2\sqrt{226}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{226}}{2*-10}=\frac{28+2\sqrt{226}}{-20}
$