(8n+5)(n-3)=245

Solution for (8n+5)(n-3)=245 equation:

(8n+5)(n-3)=245

We move all terms to the left:

(8n+5)(n-3)-(245)=0

We multiply parentheses ..

(+8n^2-24n+5n-15)-245=0

We get rid of parentheses

8n^2-24n+5n-15-245=0

We add all the numbers together, and all the variables

8n^2-19n-260=0

a = 8; b = -19; c = -260;
Δ = b2-4ac
Δ = -192-4·8·(-260)
Δ = 8681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-\sqrt{8681}}{2*8}=\frac{19-\sqrt{8681}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+\sqrt{8681}}{2*8}=\frac{19+\sqrt{8681}}{16}
$