10g=4/6g=

Solution for 10g=4/6g= equation:

10g=4/6g=

We move all terms to the left:

10g-(4/6g)=0


Domain of the equation: 6g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

10g-(+4/6g)=0

We get rid of parentheses

10g-4/6g=0

We multiply all the terms by the denominator


10g*6g-4=0

Wy multiply elements

60g^2-4=0

a = 60; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·60·(-4)
Δ = 960
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:

$\sqrt{\Delta}=\sqrt{960}=\sqrt{64*15}=\sqrt{64}*\sqrt{15}=8\sqrt{15}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{15}}{2*60}=\frac{0-8\sqrt{15}}{120}
=-\frac{8\sqrt{15}}{120}
=-\frac{\sqrt{15}}{15}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{15}}{2*60}=\frac{0+8\sqrt{15}}{120}
=\frac{8\sqrt{15}}{120}
=\frac{\sqrt{15}}{15}
$