H(x)=7/x+4

Solution for H(x)=7/x+4 equation:

(H)=7/H+4

We move all terms to the left:

(H)-(7/H+4)=0


Domain of the equation: H+4)!=0

H∈R


We get rid of parentheses

H-7/H-4=0

We multiply all the terms by the denominator


H*H-4*H-7=0

We add all the numbers together, and all the variables

-4H+H*H-7=0

Wy multiply elements

H^2-4H-7=0

a = 1; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·1·(-7)
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$H_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{11}}{2*1}=\frac{4-2\sqrt{11}}{2}
$
$H_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{11}}{2*1}=\frac{4+2\sqrt{11}}{2}
$