1/5(20x+45)-13=-3/4(24x-24)

Solution for 1/5(20x+45)-13=-3/4(24x-24) equation:

1/5(20x+45)-13=-3/4(24x-24)

We move all terms to the left:

1/5(20x+45)-13-(-3/4(24x-24))=0


Domain of the equation: 5(20x+45)!=0

x∈R



Domain of the equation: 4(24x-24))!=0

x∈R


We calculate fractions


(4x2/(5(20x+45)*4(24x-24)))+(-(-15x2)/(5(20x+45)*4(24x-24)))-13=0


We calculate terms in parentheses: +(4x2/(5(20x+45)*4(24x-24))), so:

4x2/(5(20x+45)*4(24x-24))

We multiply all the terms by the denominator


4x2

We add all the numbers together, and all the variables

4x^2

Back to the equation:

+(4x^2)



We calculate terms in parentheses: +(-(-15x2)/(5(20x+45)*4(24x-24))), so:

-(-15x2)/(5(20x+45)*4(24x-24))

We add all the numbers together, and all the variables

-(-15x^2)/(5(20x+45)*4(24x-24))

We multiply all the terms by the denominator


-(-15x^2)

We get rid of parentheses

15x^2

Back to the equation:

+(15x^2)


We add all the numbers together, and all the variables

19x^2-13=0

a = 19; b = 0; c = -13;
Δ = b2-4ac
Δ = 02-4·19·(-13)
Δ = 988
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:

$\sqrt{\Delta}=\sqrt{988}=\sqrt{4*247}=\sqrt{4}*\sqrt{247}=2\sqrt{247}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{247}}{2*19}=\frac{0-2\sqrt{247}}{38}
=-\frac{2\sqrt{247}}{38}
=-\frac{\sqrt{247}}{19}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{247}}{2*19}=\frac{0+2\sqrt{247}}{38}
=\frac{2\sqrt{247}}{38}
=\frac{\sqrt{247}}{19}
$