6n^2=42n-36

Solution for 6n^2=42n-36 equation:

6n^2=42n-36

We move all terms to the left:

6n^2-(42n-36)=0

We get rid of parentheses

6n^2-42n+36=0

a = 6; b = -42; c = +36;
Δ = b2-4ac
Δ = -422-4·6·36
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-30}{2*6}=\frac{12}{12}
=1
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+30}{2*6}=\frac{72}{12}
=6
$