4/5h-37h+12=8

Solution for 4/5h-37h+12=8 equation:

4/5h-37h+12=8

We move all terms to the left:

4/5h-37h+12-(8)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R


We add all the numbers together, and all the variables

-37h+4/5h+4=0

We multiply all the terms by the denominator


-37h*5h+4*5h+4=0

Wy multiply elements

-185h^2+20h+4=0

a = -185; b = 20; c = +4;
Δ = b2-4ac
Δ = 202-4·(-185)·4
Δ = 3360
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:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{210}}{2*-185}=\frac{-20-4\sqrt{210}}{-370}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{210}}{2*-185}=\frac{-20+4\sqrt{210}}{-370}
$