8n*n-3n+10-3n*n-6n-7=

Solution for 8n*n-3n+10-3n*n-6n-7= equation:

8n*n-3n+10-3n*n-6n-7=

We move all terms to the left:

8n*n-3n+10-3n*n-6n-7-()=0

We add all the numbers together, and all the variables

-9n+8n*n-3n*n=0

Wy multiply elements

8n^2-3n^2-9n=0

We add all the numbers together, and all the variables

5n^2-9n=0

a = 5; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·5·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*5}=\frac{0}{10}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*5}=\frac{18}{10}
=1+4/5
$