X-3/2=4/13(2x+)-1

Solution for X-3/2=4/13(2x+)-1 equation:

X-3/2=4/13(2X+)-1

We move all terms to the left:

X-3/2-(4/13(2X+)-1)=0


Domain of the equation: 13(2X+)-1)!=0

X∈R


We add all the numbers together, and all the variables

X-(4/13(+2X)-1)-3/2=0

We calculate fractions


X+()/26X+(-39X(+)/26X=0

We add all the numbers together, and all the variables

X+()/26X+(-39X0/26X=0

We multiply all the terms by the denominator


X*26X+(-39X0+()=0


We calculate terms in parentheses: +(-39X0+(), so:

-39X0+(

We add all the numbers together, and all the variables

-39X

Back to the equation:

+(-39X)


Wy multiply elements

26X^2+(-39X)=0

We get rid of parentheses

26X^2-39X=0

a = 26; b = -39; c = 0;
Δ = b2-4ac
Δ = -392-4·26·0
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-39}{2*26}=\frac{0}{52}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+39}{2*26}=\frac{78}{52}
=1+1/2
$