8/1(3-2x)=12/1(2x+13)

Solution for 8/1(3-2x)=12/1(2x+13) equation:

8/1(3-2x)=12/1(2x+13)

We move all terms to the left:

8/1(3-2x)-(12/1(2x+13))=0


Domain of the equation: 1(3-2x)!=0

x∈R



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

x∈R


We add all the numbers together, and all the variables

8/1(-2x+3)-(12/1(2x+13))=0

We calculate fractions


(8x2/(1(-2x+3)*1(2x+13)))+(-12x0/(1(-2x+3)*1(2x+13)))=0


We calculate terms in parentheses: +(8x2/(1(-2x+3)*1(2x+13))), so:

8x2/(1(-2x+3)*1(2x+13))

We multiply all the terms by the denominator


8x2

We add all the numbers together, and all the variables

8x^2

Back to the equation:

+(8x^2)



We calculate terms in parentheses: +(-12x0/(1(-2x+3)*1(2x+13))), so:

-12x0/(1(-2x+3)*1(2x+13))

We multiply all the terms by the denominator


-12x0

We add all the numbers together, and all the variables

-12x

Back to the equation:

+(-12x)


We get rid of parentheses

8x^2-12x=0

a = 8; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·8·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*8}=\frac{0}{16}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*8}=\frac{24}{16}
=1+1/2
$