5h-(3/2h+4)=10

Solution for 5h-(3/2h+4)=10 equation:

5h-(3/2h+4)=10

We move all terms to the left:

5h-(3/2h+4)-(10)=0


Domain of the equation: 2h+4)!=0

h∈R


We get rid of parentheses

5h-3/2h-4-10=0

We multiply all the terms by the denominator


5h*2h-4*2h-10*2h-3=0

Wy multiply elements

10h^2-8h-20h-3=0

We add all the numbers together, and all the variables

10h^2-28h-3=0

a = 10; b = -28; c = -3;
Δ = b2-4ac
Δ = -282-4·10·(-3)
Δ = 904
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:

$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{226}}{2*10}=\frac{28-2\sqrt{226}}{20}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{226}}{2*10}=\frac{28+2\sqrt{226}}{20}
$