15n^2-50n=8n^2-7

Solution for 15n^2-50n=8n^2-7 equation:

15n^2-50n=8n^2-7

We move all terms to the left:

15n^2-50n-(8n^2-7)=0

We get rid of parentheses

15n^2-8n^2-50n+7=0

We add all the numbers together, and all the variables

7n^2-50n+7=0

a = 7; b = -50; c = +7;
Δ = b2-4ac
Δ = -502-4·7·7
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{-(-50)-48}{2*7}=\frac{2}{14}
=1/7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+48}{2*7}=\frac{98}{14}
=7
$