4f+3=(1/2)(2f+18)

Solution for 4f+3=(1/2)(2f+18) equation:

4f+3=(1/2)(2f+18)

We move all terms to the left:

4f+3-((1/2)(2f+18))=0


Domain of the equation: 2)(2f+18))!=0

f∈R


We add all the numbers together, and all the variables

4f-((+1/2)(2f+18))+3=0

We multiply parentheses ..

-((+2f^2+1/2*18))+4f+3=0

We multiply all the terms by the denominator


-((+2f^2+1+4f*2*18))+3*2*18))=0


We calculate terms in parentheses: -((+2f^2+1+4f*2*18)), so:

(+2f^2+1+4f*2*18)

We get rid of parentheses

2f^2+4f*2*18+1

Wy multiply elements

2f^2+144f*1+1

Wy multiply elements

2f^2+144f+1

Back to the equation:

-(2f^2+144f+1)


We add all the numbers together, and all the variables

-(2f^2+144f+1)=0

We get rid of parentheses

-2f^2-144f-1=0

a = -2; b = -144; c = -1;
Δ = b2-4ac
Δ = -1442-4·(-2)·(-1)
Δ = 20728
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20728}=\sqrt{4*5182}=\sqrt{4}*\sqrt{5182}=2\sqrt{5182}$
$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-2\sqrt{5182}}{2*-2}=\frac{144-2\sqrt{5182}}{-4}
$
$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+2\sqrt{5182}}{2*-2}=\frac{144+2\sqrt{5182}}{-4}
$