7(6n2-30)=840

Solution for 7(6n2-30)=840 equation:

7(6n^2-30)=840

We move all terms to the left:

7(6n^2-30)-(840)=0

We multiply parentheses

42n^2-210-840=0

We add all the numbers together, and all the variables

42n^2-1050=0

a = 42; b = 0; c = -1050;
Δ = b2-4ac
Δ = 02-4·42·(-1050)
Δ = 176400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{176400}=420$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-420}{2*42}=\frac{-420}{84}
=-5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+420}{2*42}=\frac{420}{84}
=5
$