2h(6h-5)=1

Solution for 2h(6h-5)=1 equation:

2h(6h-5)=1

We move all terms to the left:

2h(6h-5)-(1)=0

We multiply parentheses

12h^2-10h-1=0

a = 12; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·12·(-1)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{37}}{2*12}=\frac{10-2\sqrt{37}}{24}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{37}}{2*12}=\frac{10+2\sqrt{37}}{24}
$