(9a+4)=(3a^2-0.75)

Solution for (9a+4)=(3a^2-0.75) equation:

(9a+4)=(3a^2-0.75)

We move all terms to the left:

(9a+4)-((3a^2-0.75))=0

We get rid of parentheses

9a-((3a^2-0.75))+4=0


We calculate terms in parentheses: -((3a^2-0.75)), so:

(3a^2-0.75)

We get rid of parentheses

3a^2-0.75

Back to the equation:

-(3a^2-0.75)


We get rid of parentheses

-3a^2+9a+0.75+4=0

We add all the numbers together, and all the variables

-3a^2+9a+4.75=0

a = -3; b = 9; c = +4.75;
Δ = b2-4ac
Δ = 92-4·(-3)·4.75
Δ = 138
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{-(9)-\sqrt{138}}{2*-3}=\frac{-9-\sqrt{138}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{138}}{2*-3}=\frac{-9+\sqrt{138}}{-6}
$