g(-5/3)=-5/3

Solution for g(-5/3)=-5/3 equation:

g(-5/3)=-5/3

We move all terms to the left:

g(-5/3)-(-5/3)=0

We multiply parentheses

-5g^2-(-5/3)=0

We get rid of parentheses

-5g^2+5/3=0

We multiply all the terms by the denominator


-5g^2*3+5=0

Wy multiply elements

-15g^2+5=0

a = -15; b = 0; c = +5;
Δ = b2-4ac
Δ = 02-4·(-15)·5
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{3}}{2*-15}=\frac{0-10\sqrt{3}}{-30}
=-\frac{10\sqrt{3}}{-30}
=-\frac{\sqrt{3}}{-3}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{3}}{2*-15}=\frac{0+10\sqrt{3}}{-30}
=\frac{10\sqrt{3}}{-30}
=\frac{\sqrt{3}}{-3}
$