3.5-2g=1/2g-4

Solution for 3.5-2g=1/2g-4 equation:

3.5-2g=1/2g-4

We move all terms to the left:

3.5-2g-(1/2g-4)=0


Domain of the equation: 2g-4)!=0

g∈R


We get rid of parentheses

-2g-1/2g+4+3.5=0

We multiply all the terms by the denominator


-2g*2g+4*2g+(3.5)*2g-1=0

We multiply parentheses

-2g*2g+4*2g+7g-1=0

Wy multiply elements

-4g^2+8g+7g-1=0

We add all the numbers together, and all the variables

-4g^2+15g-1=0

a = -4; b = 15; c = -1;
Δ = b2-4ac
Δ = 152-4·(-4)·(-1)
Δ = 209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$g_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{209}}{2*-4}=\frac{-15-\sqrt{209}}{-8}
$
$g_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{209}}{2*-4}=\frac{-15+\sqrt{209}}{-8}
$