H(x)=3/4x-2

Solution for H(x)=3/4x-2 equation:

(H)=3/4H-2

We move all terms to the left:

(H)-(3/4H-2)=0


Domain of the equation: 4H-2)!=0

H∈R


We get rid of parentheses

H-3/4H+2=0

We multiply all the terms by the denominator


H*4H+2*4H-3=0

Wy multiply elements

4H^2+8H-3=0

a = 4; b = 8; c = -3;
Δ = b2-4ac
Δ = 82-4·4·(-3)
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{7}}{2*4}=\frac{-8-4\sqrt{7}}{8}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{7}}{2*4}=\frac{-8+4\sqrt{7}}{8}
$