3(5+a)=(1/4)(28+12a)

Solution for 3(5+a)=(1/4)(28+12a) equation:

3(5+a)=(1/4)(28+12a)

We move all terms to the left:

3(5+a)-((1/4)(28+12a))=0


Domain of the equation: 4)(28+12a))!=0

a∈R


We add all the numbers together, and all the variables

3(a+5)-((+1/4)(12a+28))=0

We multiply parentheses

3a-((+1/4)(12a+28))+15=0

We multiply parentheses ..

-((+12a^2+1/4*28))+3a+15=0

We multiply all the terms by the denominator


-((+12a^2+1+3a*4*28))+15*4*28))=0


We calculate terms in parentheses: -((+12a^2+1+3a*4*28)), so:

(+12a^2+1+3a*4*28)

We get rid of parentheses

12a^2+3a*4*28+1

Wy multiply elements

12a^2+336a*2+1

Wy multiply elements

12a^2+672a+1

Back to the equation:

-(12a^2+672a+1)


We add all the numbers together, and all the variables

-(12a^2+672a+1)=0

We get rid of parentheses

-12a^2-672a-1=0

a = -12; b = -672; c = -1;
Δ = b2-4ac
Δ = -6722-4·(-12)·(-1)
Δ = 451536
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{451536}=\sqrt{16*28221}=\sqrt{16}*\sqrt{28221}=4\sqrt{28221}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-672)-4\sqrt{28221}}{2*-12}=\frac{672-4\sqrt{28221}}{-24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-672)+4\sqrt{28221}}{2*-12}=\frac{672+4\sqrt{28221}}{-24}
$