35n^2+8n-9=7

Solution for 35n^2+8n-9=7 equation:

35n^2+8n-9=7

We move all terms to the left:

35n^2+8n-9-(7)=0

We add all the numbers together, and all the variables

35n^2+8n-16=0

a = 35; b = 8; c = -16;
Δ = b2-4ac
Δ = 82-4·35·(-16)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-48}{2*35}=\frac{-56}{70}
=-4/5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+48}{2*35}=\frac{40}{70}
=4/7
$