6a^2+5a+4=3

Solution for 6a^2+5a+4=3 equation:

6a^2+5a+4=3

We move all terms to the left:

6a^2+5a+4-(3)=0

We add all the numbers together, and all the variables

6a^2+5a+1=0

a = 6; b = 5; c = +1;
Δ = b2-4ac
Δ = 52-4·6·1
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-1}{2*6}=\frac{-6}{12}
=-1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+1}{2*6}=\frac{-4}{12}
=-1/3
$