7n+12=(1/2)(14n+24)

Solution for 7n+12=(1/2)(14n+24) equation:

7n+12=(1/2)(14n+24)

We move all terms to the left:

7n+12-((1/2)(14n+24))=0


Domain of the equation: 2)(14n+24))!=0

n∈R


We add all the numbers together, and all the variables

7n-((+1/2)(14n+24))+12=0

We multiply parentheses ..

-((+14n^2+1/2*24))+7n+12=0

We multiply all the terms by the denominator


-((+14n^2+1+7n*2*24))+12*2*24))=0


We calculate terms in parentheses: -((+14n^2+1+7n*2*24)), so:

(+14n^2+1+7n*2*24)

We get rid of parentheses

14n^2+7n*2*24+1

Wy multiply elements

14n^2+336n*2+1

Wy multiply elements

14n^2+672n+1

Back to the equation:

-(14n^2+672n+1)


We add all the numbers together, and all the variables

-(14n^2+672n+1)=0

We get rid of parentheses

-14n^2-672n-1=0

a = -14; b = -672; c = -1;
Δ = b2-4ac
Δ = -6722-4·(-14)·(-1)
Δ = 451528
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{451528}=\sqrt{4*112882}=\sqrt{4}*\sqrt{112882}=2\sqrt{112882}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-672)-2\sqrt{112882}}{2*-14}=\frac{672-2\sqrt{112882}}{-28}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-672)+2\sqrt{112882}}{2*-14}=\frac{672+2\sqrt{112882}}{-28}
$