19-g=7/g=15

Solution for 19-g=7/g=15 equation:

19-g=7/g=15

We move all terms to the left:

19-g-(7/g)=0


Domain of the equation: g)!=0

g!=0/1

g!=0

g∈R


We add all the numbers together, and all the variables

-g-(+7/g)+19=0

We add all the numbers together, and all the variables

-1g-(+7/g)+19=0

We get rid of parentheses

-1g-7/g+19=0

We multiply all the terms by the denominator


-1g*g+19*g-7=0

We add all the numbers together, and all the variables

19g-1g*g-7=0

Wy multiply elements

-1g^2+19g-7=0

a = -1; b = 19; c = -7;
Δ = b2-4ac
Δ = 192-4·(-1)·(-7)
Δ = 333
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:

$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(19)-3\sqrt{37}}{2*-1}=\frac{-19-3\sqrt{37}}{-2}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+3\sqrt{37}}{2*-1}=\frac{-19+3\sqrt{37}}{-2}
$