8+7/10h=6+1.5h

Solution for 8+7/10h=6+1.5h equation:

8+7/10h=6+1.5h

We move all terms to the left:

8+7/10h-(6+1.5h)=0


Domain of the equation: 10h!=0

h!=0/10

h!=0

h∈R


We add all the numbers together, and all the variables

7/10h-(1.5h+6)+8=0

We get rid of parentheses

7/10h-1.5h-6+8=0

We multiply all the terms by the denominator


-(1.5h)*10h-6*10h+8*10h+7=0

We add all the numbers together, and all the variables

-(+1.5h)*10h-6*10h+8*10h+7=0

We multiply parentheses

-10h^2-6*10h+8*10h+7=0

Wy multiply elements

-10h^2-60h+80h+7=0

We add all the numbers together, and all the variables

-10h^2+20h+7=0

a = -10; b = 20; c = +7;
Δ = b2-4ac
Δ = 202-4·(-10)·7
Δ = 680
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:

$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{170}}{2*-10}=\frac{-20-2\sqrt{170}}{-20}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{170}}{2*-10}=\frac{-20+2\sqrt{170}}{-20}
$