1=3a-4/2a+6

Solution for 1=3a-4/2a+6 equation:

1=3a-4/2a+6

We move all terms to the left:

1-(3a-4/2a+6)=0


Domain of the equation: 2a+6)!=0

a∈R


We get rid of parentheses

-3a+4/2a-6+1=0

We multiply all the terms by the denominator


-3a*2a-6*2a+1*2a+4=0

Wy multiply elements

-6a^2-12a+2a+4=0

We add all the numbers together, and all the variables

-6a^2-10a+4=0

a = -6; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·(-6)·4
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-14}{2*-6}=\frac{-4}{-12}
=1/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+14}{2*-6}=\frac{24}{-12}
=-2
$