4/5*g=40

Solution for 4/5*g=40 equation:

4/5*g=40

We move all terms to the left:

4/5*g-(40)=0


Domain of the equation: 5*g!=0

g!=0/1

g!=0

g∈R


We multiply all the terms by the denominator


-40*5*g+4=0

Wy multiply elements

-200g*g+4=0

Wy multiply elements

-200g^2+4=0

a = -200; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-200)·4
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*-200}=\frac{0-40\sqrt{2}}{-400}
=-\frac{40\sqrt{2}}{-400}
=-\frac{\sqrt{2}}{-10}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*-200}=\frac{0+40\sqrt{2}}{-400}
=\frac{40\sqrt{2}}{-400}
=\frac{\sqrt{2}}{-10}
$