H(x)=3/8x-6

Solution for H(x)=3/8x-6 equation:

(H)=3/8H-6

We move all terms to the left:

(H)-(3/8H-6)=0


Domain of the equation: 8H-6)!=0

H∈R


We get rid of parentheses

H-3/8H+6=0

We multiply all the terms by the denominator


H*8H+6*8H-3=0

Wy multiply elements

8H^2+48H-3=0

a = 8; b = 48; c = -3;
Δ = b2-4ac
Δ = 482-4·8·(-3)
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(48)-20\sqrt{6}}{2*8}=\frac{-48-20\sqrt{6}}{16}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(48)+20\sqrt{6}}{2*8}=\frac{-48+20\sqrt{6}}{16}
$