4n+6n(n-15)=7n-2(n-8)

Solution for 4n+6n(n-15)=7n-2(n-8) equation:

4n+6n(n-15)=7n-2(n-8)

We move all terms to the left:

4n+6n(n-15)-(7n-2(n-8))=0

We multiply parentheses

6n^2+4n-90n-(7n-2(n-8))=0


We calculate terms in parentheses: -(7n-2(n-8)), so:

7n-2(n-8)

We multiply parentheses

7n-2n+16

We add all the numbers together, and all the variables

5n+16

Back to the equation:

-(5n+16)


We add all the numbers together, and all the variables

6n^2-86n-(5n+16)=0

We get rid of parentheses

6n^2-86n-5n-16=0

We add all the numbers together, and all the variables

6n^2-91n-16=0

a = 6; b = -91; c = -16;
Δ = b2-4ac
Δ = -912-4·6·(-16)
Δ = 8665
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-\sqrt{8665}}{2*6}=\frac{91-\sqrt{8665}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+\sqrt{8665}}{2*6}=\frac{91+\sqrt{8665}}{12}
$