-4(x+5)=(5/3)(3x-12)

Solution for -4(x+5)=(5/3)(3x-12) equation:

-4(x+5)=(5/3)(3x-12)

We move all terms to the left:

-4(x+5)-((5/3)(3x-12))=0


Domain of the equation: 3)(3x-12))!=0

x∈R


We add all the numbers together, and all the variables

-4(x+5)-((+5/3)(3x-12))=0

We multiply parentheses

-4x-((+5/3)(3x-12))-20=0

We multiply parentheses ..

-((+15x^2+5/3*-12))-4x-20=0

We multiply all the terms by the denominator


-((+15x^2+5-4x*3*-12))-20*3*-12))=0


We calculate terms in parentheses: -((+15x^2+5-4x*3*-12)), so:

(+15x^2+5-4x*3*-12)

We get rid of parentheses

15x^2-4x*3*+5-12

We add all the numbers together, and all the variables

15x^2-4x*3*-7

Wy multiply elements

15x^2-12x^2-7

We add all the numbers together, and all the variables

3x^2-7

Back to the equation:

-(3x^2-7)


We add all the numbers together, and all the variables

-(3x^2-7)=0

We get rid of parentheses

-3x^2+7=0

a = -3; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-3)·7
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{21}}{2*-3}=\frac{0-2\sqrt{21}}{-6}
=-\frac{2\sqrt{21}}{-6}
=-\frac{\sqrt{21}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{21}}{2*-3}=\frac{0+2\sqrt{21}}{-6}
=\frac{2\sqrt{21}}{-6}
=\frac{\sqrt{21}}{-3}
$