4/5(25x+10)-9=-1/4(24x-16)

Solution for 4/5(25x+10)-9=-1/4(24x-16) equation:

4/5(25x+10)-9=-1/4(24x-16)

We move all terms to the left:

4/5(25x+10)-9-(-1/4(24x-16))=0


Domain of the equation: 5(25x+10)!=0

x∈R



Domain of the equation: 4(24x-16))!=0

x∈R


We calculate fractions


(16x2/(5(25x+10)*4(24x-16)))+(-(-5x2)/(5(25x+10)*4(24x-16)))-9=0


We calculate terms in parentheses: +(16x2/(5(25x+10)*4(24x-16))), so:

16x2/(5(25x+10)*4(24x-16))

We multiply all the terms by the denominator


16x2

We add all the numbers together, and all the variables

16x^2

Back to the equation:

+(16x^2)



We calculate terms in parentheses: +(-(-5x2)/(5(25x+10)*4(24x-16))), so:

-(-5x2)/(5(25x+10)*4(24x-16))

We add all the numbers together, and all the variables

-(-5x^2)/(5(25x+10)*4(24x-16))

We multiply all the terms by the denominator


-(-5x^2)

We get rid of parentheses

5x^2

Back to the equation:

+(5x^2)


We add all the numbers together, and all the variables

21x^2-9=0

a = 21; b = 0; c = -9;
Δ = b2-4ac
Δ = 02-4·21·(-9)
Δ = 756
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:

$\sqrt{\Delta}=\sqrt{756}=\sqrt{36*21}=\sqrt{36}*\sqrt{21}=6\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{21}}{2*21}=\frac{0-6\sqrt{21}}{42}
=-\frac{6\sqrt{21}}{42}
=-\frac{\sqrt{21}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{21}}{2*21}=\frac{0+6\sqrt{21}}{42}
=\frac{6\sqrt{21}}{42}
=\frac{\sqrt{21}}{7}
$