a+3/2(a)=30

Solution for a+3/2(a)=30 equation:

a+3/2(a)=30

We move all terms to the left:

a+3/2(a)-(30)=0


Domain of the equation: 2a!=0

a!=0/2

a!=0

a∈R


We multiply all the terms by the denominator


a*2a-30*2a+3=0

Wy multiply elements

2a^2-60a+3=0

a = 2; b = -60; c = +3;
Δ = b2-4ac
Δ = -602-4·2·3
Δ = 3576
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:

$\sqrt{\Delta}=\sqrt{3576}=\sqrt{4*894}=\sqrt{4}*\sqrt{894}=2\sqrt{894}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{894}}{2*2}=\frac{60-2\sqrt{894}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{894}}{2*2}=\frac{60+2\sqrt{894}}{4}
$