2/5h+10=6h

Solution for 2/5h+10=6h equation:

2/5h+10=6h

We move all terms to the left:

2/5h+10-(6h)=0


Domain of the equation: 5h!=0

h!=0/5

h!=0

h∈R


We add all the numbers together, and all the variables

-6h+2/5h+10=0

We multiply all the terms by the denominator


-6h*5h+10*5h+2=0

Wy multiply elements

-30h^2+50h+2=0

a = -30; b = 50; c = +2;
Δ = b2-4ac
Δ = 502-4·(-30)·2
Δ = 2740
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:

$\sqrt{\Delta}=\sqrt{2740}=\sqrt{4*685}=\sqrt{4}*\sqrt{685}=2\sqrt{685}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{685}}{2*-30}=\frac{-50-2\sqrt{685}}{-60}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{685}}{2*-30}=\frac{-50+2\sqrt{685}}{-60}
$