3(4a2)=2(a+2)

Solution for 3(4a2)=2(a+2) equation:

3(4a^2)=2(a+2)

We move all terms to the left:

3(4a^2)-(2(a+2))=0


We calculate terms in parentheses: -(2(a+2)), so:

2(a+2)

We multiply parentheses

2a+4

Back to the equation:

-(2a+4)


We get rid of parentheses

34a^2-2a-4=0

a = 34; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·34·(-4)
Δ = 548
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:

$\sqrt{\Delta}=\sqrt{548}=\sqrt{4*137}=\sqrt{4}*\sqrt{137}=2\sqrt{137}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{137}}{2*34}=\frac{2-2\sqrt{137}}{68}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{137}}{2*34}=\frac{2+2\sqrt{137}}{68}
$