59(g+18)=1/6g+3

Solution for 59(g+18)=1/6g+3 equation:

59(g+18)=1/6g+3

We move all terms to the left:

59(g+18)-(1/6g+3)=0


Domain of the equation: 6g+3)!=0

g∈R


We multiply parentheses

59g-(1/6g+3)+1062=0

We get rid of parentheses

59g-1/6g-3+1062=0

We multiply all the terms by the denominator


59g*6g-3*6g+1062*6g-1=0

Wy multiply elements

354g^2-18g+6372g-1=0

We add all the numbers together, and all the variables

354g^2+6354g-1=0

a = 354; b = 6354; c = -1;
Δ = b2-4ac
Δ = 63542-4·354·(-1)
Δ = 40374732
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:

$\sqrt{\Delta}=\sqrt{40374732}=\sqrt{4*10093683}=\sqrt{4}*\sqrt{10093683}=2\sqrt{10093683}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6354)-2\sqrt{10093683}}{2*354}=\frac{-6354-2\sqrt{10093683}}{708}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6354)+2\sqrt{10093683}}{2*354}=\frac{-6354+2\sqrt{10093683}}{708}
$