-2n-3(5n-7)=-3n(n-6)-2

Solution for -2n-3(5n-7)=-3n(n-6)-2 equation:

-2n-3(5n-7)=-3n(n-6)-2

We move all terms to the left:

-2n-3(5n-7)-(-3n(n-6)-2)=0

We multiply parentheses

-2n-15n-(-3n(n-6)-2)+21=0


We calculate terms in parentheses: -(-3n(n-6)-2), so:

-3n(n-6)-2

We multiply parentheses

-3n^2+18n-2

Back to the equation:

-(-3n^2+18n-2)


We add all the numbers together, and all the variables

-(-3n^2+18n-2)-17n+21=0

We get rid of parentheses

3n^2-18n-17n+2+21=0

We add all the numbers together, and all the variables

3n^2-35n+23=0

a = 3; b = -35; c = +23;
Δ = b2-4ac
Δ = -352-4·3·23
Δ = 949
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{-(-35)-\sqrt{949}}{2*3}=\frac{35-\sqrt{949}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{949}}{2*3}=\frac{35+\sqrt{949}}{6}
$