6H+2=34h2-4h-2

Solution for 6H+2=34h2-4h-2 equation:

6+2=34H^2-4H-2

We move all terms to the left:

6+2-(34H^2-4H-2)=0

We add all the numbers together, and all the variables

-(34H^2-4H-2)+8=0

We get rid of parentheses

-34H^2+4H+2+8=0

We add all the numbers together, and all the variables

-34H^2+4H+10=0

a = -34; b = 4; c = +10;
Δ = b2-4ac
Δ = 42-4·(-34)·10
Δ = 1376
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1376}=\sqrt{16*86}=\sqrt{16}*\sqrt{86}=4\sqrt{86}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{86}}{2*-34}=\frac{-4-4\sqrt{86}}{-68}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{86}}{2*-34}=\frac{-4+4\sqrt{86}}{-68}
$