(1/2)(4h+14)=4h+1

Solution for (1/2)(4h+14)=4h+1 equation:

(1/2)(4h+14)=4h+1

We move all terms to the left:

(1/2)(4h+14)-(4h+1)=0


Domain of the equation: 2)(4h+14)!=0

h∈R


We add all the numbers together, and all the variables

(+1/2)(4h+14)-(4h+1)=0

We get rid of parentheses

(+1/2)(4h+14)-4h-1=0

We multiply parentheses ..

(+4h^2+1/2*14)-4h-1=0

We multiply all the terms by the denominator


(+4h^2+1-4h*2*14)-1*2*14)=0

We add all the numbers together, and all the variables

(+4h^2+1-4h*2*14)=0

We get rid of parentheses

4h^2-4h*2*14+1=0

Wy multiply elements

4h^2-112h*1+1=0

Wy multiply elements

4h^2-112h+1=0

a = 4; b = -112; c = +1;
Δ = b2-4ac
Δ = -1122-4·4·1
Δ = 12528
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:

$\sqrt{\Delta}=\sqrt{12528}=\sqrt{144*87}=\sqrt{144}*\sqrt{87}=12\sqrt{87}$
$h_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-12\sqrt{87}}{2*4}=\frac{112-12\sqrt{87}}{8}
$
$h_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+12\sqrt{87}}{2*4}=\frac{112+12\sqrt{87}}{8}
$