1=8m^2-6m-14

Solution for 1=8m^2-6m-14 equation:

1=8m^2-6m-14

We move all terms to the left:

1-(8m^2-6m-14)=0

We get rid of parentheses

-8m^2+6m+14+1=0

We add all the numbers together, and all the variables

-8m^2+6m+15=0

a = -8; b = 6; c = +15;
Δ = b2-4ac
Δ = 62-4·(-8)·15
Δ = 516
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$m_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{129}}{2*-8}=\frac{-6-2\sqrt{129}}{-16}
$
$m_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{129}}{2*-8}=\frac{-6+2\sqrt{129}}{-16}
$