2/3(24x+21)-7=-1/5(20x-30)

Solution for 2/3(24x+21)-7=-1/5(20x-30) equation:

2/3(24x+21)-7=-1/5(20x-30)

We move all terms to the left:

2/3(24x+21)-7-(-1/5(20x-30))=0


Domain of the equation: 3(24x+21)!=0

x∈R



Domain of the equation: 5(20x-30))!=0

x∈R


We calculate fractions


(10x2/(3(24x+21)*5(20x-30)))+(-(-3x2)/(3(24x+21)*5(20x-30)))-7=0


We calculate terms in parentheses: +(10x2/(3(24x+21)*5(20x-30))), so:

10x2/(3(24x+21)*5(20x-30))

We multiply all the terms by the denominator


10x2

We add all the numbers together, and all the variables

10x^2

Back to the equation:

+(10x^2)



We calculate terms in parentheses: +(-(-3x2)/(3(24x+21)*5(20x-30))), so:

-(-3x2)/(3(24x+21)*5(20x-30))

We add all the numbers together, and all the variables

-(-3x^2)/(3(24x+21)*5(20x-30))

We multiply all the terms by the denominator


-(-3x^2)

We get rid of parentheses

3x^2

Back to the equation:

+(3x^2)


We add all the numbers together, and all the variables

13x^2-7=0

a = 13; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·13·(-7)
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{91}}{2*13}=\frac{0-2\sqrt{91}}{26}
=-\frac{2\sqrt{91}}{26}
=-\frac{\sqrt{91}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{91}}{2*13}=\frac{0+2\sqrt{91}}{26}
=\frac{2\sqrt{91}}{26}
=\frac{\sqrt{91}}{13}
$