4=g(g-7)

Solution for 4=g(g-7) equation:

4=g(g-7)

We move all terms to the left:

4-(g(g-7))=0


We calculate terms in parentheses: -(g(g-7)), so:

g(g-7)

We multiply parentheses

g^2-7g

Back to the equation:

-(g^2-7g)


We get rid of parentheses

-g^2+7g+4=0

We add all the numbers together, and all the variables

-1g^2+7g+4=0

a = -1; b = 7; c = +4;
Δ = b2-4ac
Δ = 72-4·(-1)·4
Δ = 65
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{65}}{2*-1}=\frac{-7-\sqrt{65}}{-2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{65}}{2*-1}=\frac{-7+\sqrt{65}}{-2}
$