1/4g+102+5/8g-6=180

Solution for 1/4g+102+5/8g-6=180 equation:

1/4g+102+5/8g-6=180

We move all terms to the left:

1/4g+102+5/8g-6-(180)=0


Domain of the equation: 4g!=0

g!=0/4

g!=0

g∈R



Domain of the equation: 8g!=0

g!=0/8

g!=0

g∈R


We add all the numbers together, and all the variables

1/4g+5/8g-84=0

We calculate fractions


8g/32g^2+20g/32g^2-84=0

We multiply all the terms by the denominator


8g+20g-84*32g^2=0

We add all the numbers together, and all the variables

28g-84*32g^2=0

Wy multiply elements

-2688g^2+28g=0

a = -2688; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·(-2688)·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*-2688}=\frac{-56}{-5376}
=1/96
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*-2688}=\frac{0}{-5376}
=0
$