h=7/4h-1.5=

Solution for h=7/4h-1.5= equation:

h=7/4h-1.5=

We move all terms to the left:

h-(7/4h-1.5)=0


Domain of the equation: 4h-1.5)!=0

h∈R


We get rid of parentheses

h-7/4h+1.5=0

We multiply all the terms by the denominator


h*4h+(1.5)*4h-7=0

We multiply parentheses

h*4h+6h-7=0

Wy multiply elements

4h^2+6h-7=0

a = 4; b = 6; c = -7;
Δ = b2-4ac
Δ = 62-4·4·(-7)
Δ = 148
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:

$\sqrt{\Delta}=\sqrt{148}=\sqrt{4*37}=\sqrt{4}*\sqrt{37}=2\sqrt{37}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{37}}{2*4}=\frac{-6-2\sqrt{37}}{8}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{37}}{2*4}=\frac{-6+2\sqrt{37}}{8}
$