5n^2+7n-8=8

Solution for 5n^2+7n-8=8 equation:

5n^2+7n-8=8

We move all terms to the left:

5n^2+7n-8-(8)=0

We add all the numbers together, and all the variables

5n^2+7n-16=0

a = 5; b = 7; c = -16;
Δ = b2-4ac
Δ = 72-4·5·(-16)
Δ = 369
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{41}}{2*5}=\frac{-7-3\sqrt{41}}{10}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{41}}{2*5}=\frac{-7+3\sqrt{41}}{10}
$