6(3r-4)=(3/8)(46r+8)

Solution for 6(3r-4)=(3/8)(46r+8) equation:

6(3r-4)=(3/8)(46r+8)

We move all terms to the left:

6(3r-4)-((3/8)(46r+8))=0


Domain of the equation: 8)(46r+8))!=0

r∈R


We add all the numbers together, and all the variables

6(3r-4)-((+3/8)(46r+8))=0

We multiply parentheses

18r-((+3/8)(46r+8))-24=0

We multiply parentheses ..

-((+138r^2+3/8*8))+18r-24=0

We multiply all the terms by the denominator


-((+138r^2+3+18r*8*8))-24*8*8))=0


We calculate terms in parentheses: -((+138r^2+3+18r*8*8)), so:

(+138r^2+3+18r*8*8)

We get rid of parentheses

138r^2+18r*8*8+3

Wy multiply elements

138r^2+1152r*8+3

Wy multiply elements

138r^2+9216r+3

Back to the equation:

-(138r^2+9216r+3)


We add all the numbers together, and all the variables

-(138r^2+9216r+3)=0

We get rid of parentheses

-138r^2-9216r-3=0

a = -138; b = -9216; c = -3;
Δ = b2-4ac
Δ = -92162-4·(-138)·(-3)
Δ = 84933000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{84933000}=\sqrt{900*94370}=\sqrt{900}*\sqrt{94370}=30\sqrt{94370}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9216)-30\sqrt{94370}}{2*-138}=\frac{9216-30\sqrt{94370}}{-276}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9216)+30\sqrt{94370}}{2*-138}=\frac{9216+30\sqrt{94370}}{-276}
$