5/9g+10=16g+3

Solution for 5/9g+10=16g+3 equation:

5/9g+10=16g+3

We move all terms to the left:

5/9g+10-(16g+3)=0


Domain of the equation: 9g!=0

g!=0/9

g!=0

g∈R


We get rid of parentheses

5/9g-16g-3+10=0

We multiply all the terms by the denominator


-16g*9g-3*9g+10*9g+5=0

Wy multiply elements

-144g^2-27g+90g+5=0

We add all the numbers together, and all the variables

-144g^2+63g+5=0

a = -144; b = 63; c = +5;
Δ = b2-4ac
Δ = 632-4·(-144)·5
Δ = 6849
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:

$\sqrt{\Delta}=\sqrt{6849}=\sqrt{9*761}=\sqrt{9}*\sqrt{761}=3\sqrt{761}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-3\sqrt{761}}{2*-144}=\frac{-63-3\sqrt{761}}{-288}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+3\sqrt{761}}{2*-144}=\frac{-63+3\sqrt{761}}{-288}
$