21+2+g(23+g)=21+3(g+34)

Solution for 21+2+g(23+g)=21+3(g+34) equation:

21+2+g(23+g)=21+3(g+34)

We move all terms to the left:

21+2+g(23+g)-(21+3(g+34))=0

We add all the numbers together, and all the variables

g(g+23)-(21+3(g+34))+21+2=0

We add all the numbers together, and all the variables

g(g+23)-(21+3(g+34))+23=0

We multiply parentheses

g^2+23g-(21+3(g+34))+23=0


We calculate terms in parentheses: -(21+3(g+34)), so:

21+3(g+34)

determiningTheFunctionDomain
3(g+34)+21

We multiply parentheses

3g+102+21

We add all the numbers together, and all the variables

3g+123

Back to the equation:

-(3g+123)


We get rid of parentheses

g^2+23g-3g-123+23=0

We add all the numbers together, and all the variables

g^2+20g-100=0

a = 1; b = 20; c = -100;
Δ = b2-4ac
Δ = 202-4·1·(-100)
Δ = 800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20\sqrt{2}}{2*1}=\frac{-20-20\sqrt{2}}{2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20\sqrt{2}}{2*1}=\frac{-20+20\sqrt{2}}{2}
$