6n2+8n-7=0

Solution for 6n2+8n-7=0 equation:

6n^2+8n-7=0

a = 6; b = 8; c = -7;
Δ = b2-4ac
Δ = 82-4·6·(-7)
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{58}}{2*6}=\frac{-8-2\sqrt{58}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{58}}{2*6}=\frac{-8+2\sqrt{58}}{12}
$