6h^2+2h=3/4

Solution for 6h^2+2h=3/4 equation:

6h^2+2h=3/4

We move all terms to the left:

6h^2+2h-(3/4)=0

We add all the numbers together, and all the variables

6h^2+2h-(+3/4)=0

We get rid of parentheses

6h^2+2h-3/4=0

We multiply all the terms by the denominator


6h^2*4+2h*4-3=0

Wy multiply elements

24h^2+8h-3=0

a = 24; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·24·(-3)
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{22}}{2*24}=\frac{-8-4\sqrt{22}}{48}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{22}}{2*24}=\frac{-8+4\sqrt{22}}{48}
$