-1/2(-12x+576)=6/5(25x+50)

Solution for -1/2(-12x+576)=6/5(25x+50) equation:

-1/2(-12x+576)=6/5(25x+50)

We move all terms to the left:

-1/2(-12x+576)-(6/5(25x+50))=0


Domain of the equation: 2(-12x+576)!=0

x∈R



Domain of the equation: 5(25x+50))!=0

x∈R


We calculate fractions


(-5x2/(2(-12x+576)*5(25x+50)))+(-12x0/(2(-12x+576)*5(25x+50)))=0


We calculate terms in parentheses: +(-5x2/(2(-12x+576)*5(25x+50))), so:

-5x2/(2(-12x+576)*5(25x+50))

We multiply all the terms by the denominator


-5x2

We add all the numbers together, and all the variables

-5x^2

Back to the equation:

+(-5x^2)



We calculate terms in parentheses: +(-12x0/(2(-12x+576)*5(25x+50))), so:

-12x0/(2(-12x+576)*5(25x+50))

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

-5x^2-12x=0

a = -5; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·(-5)·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*-5}=\frac{0}{-10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*-5}=\frac{24}{-10}
=-2+2/5
$