(5a+3)=(4a^2-0.75)

Solution for (5a+3)=(4a^2-0.75) equation:

(5a+3)=(4a^2-0.75)

We move all terms to the left:

(5a+3)-((4a^2-0.75))=0

We get rid of parentheses

5a-((4a^2-0.75))+3=0


We calculate terms in parentheses: -((4a^2-0.75)), so:

(4a^2-0.75)

We get rid of parentheses

4a^2-0.75

Back to the equation:

-(4a^2-0.75)


We get rid of parentheses

-4a^2+5a+0.75+3=0

We add all the numbers together, and all the variables

-4a^2+5a+3.75=0

a = -4; b = 5; c = +3.75;
Δ = b2-4ac
Δ = 52-4·(-4)·3.75
Δ = 85
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{-(5)-\sqrt{85}}{2*-4}=\frac{-5-\sqrt{85}}{-8}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{85}}{2*-4}=\frac{-5+\sqrt{85}}{-8}
$