3/2a-11+a=4a-2

Solution for 3/2a-11+a=4a-2 equation:

3/2a-11+a=4a-2

We move all terms to the left:

3/2a-11+a-(4a-2)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We add all the numbers together, and all the variables

a+3/2a-(4a-2)-11=0

We get rid of parentheses

a+3/2a-4a+2-11=0

We multiply all the terms by the denominator


a*2a-4a*2a+2*2a-11*2a+3=0

Wy multiply elements

2a^2-8a^2+4a-22a+3=0

We add all the numbers together, and all the variables

-6a^2-18a+3=0

a = -6; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·(-6)·3
Δ = 396
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{11}}{2*-6}=\frac{18-6\sqrt{11}}{-12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{11}}{2*-6}=\frac{18+6\sqrt{11}}{-12}
$