4a^2-2=3(a+1)

Solution for 4a^2-2=3(a+1) equation:

4a^2-2=3(a+1)

We move all terms to the left:

4a^2-2-(3(a+1))=0


We calculate terms in parentheses: -(3(a+1)), so:

3(a+1)

We multiply parentheses

3a+3

Back to the equation:

-(3a+3)


We get rid of parentheses

4a^2-3a-3-2=0

We add all the numbers together, and all the variables

4a^2-3a-5=0

a = 4; b = -3; c = -5;
Δ = b2-4ac
Δ = -32-4·4·(-5)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{89}}{2*4}=\frac{3-\sqrt{89}}{8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*4}=\frac{3+\sqrt{89}}{8}
$