7(h-5)-3h=3/2h

Solution for 7(h-5)-3h=3/2h equation:

7(h-5)-3h=3/2h

We move all terms to the left:

7(h-5)-3h-(3/2h)=0


Domain of the equation: 2h)!=0

h!=0/1

h!=0

h∈R


We add all the numbers together, and all the variables

7(h-5)-3h-(+3/2h)=0

We add all the numbers together, and all the variables

-3h+7(h-5)-(+3/2h)=0

We multiply parentheses

-3h+7h-(+3/2h)-35=0

We get rid of parentheses

-3h+7h-3/2h-35=0

We multiply all the terms by the denominator


-3h*2h+7h*2h-35*2h-3=0

Wy multiply elements

-6h^2+14h^2-70h-3=0

We add all the numbers together, and all the variables

8h^2-70h-3=0

a = 8; b = -70; c = -3;
Δ = b2-4ac
Δ = -702-4·8·(-3)
Δ = 4996
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:

$\sqrt{\Delta}=\sqrt{4996}=\sqrt{4*1249}=\sqrt{4}*\sqrt{1249}=2\sqrt{1249}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-70)-2\sqrt{1249}}{2*8}=\frac{70-2\sqrt{1249}}{16}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-70)+2\sqrt{1249}}{2*8}=\frac{70+2\sqrt{1249}}{16}
$