4/3=a2+5a+6

Solution for 4/3=a2+5a+6 equation:

4/3=a2+5a+6

We move all terms to the left:

4/3-(a2+5a+6)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

-a^2-5a-6+4/3=0

We multiply all the terms by the denominator


-a^2*3-5a*3+4-6*3=0

We add all the numbers together, and all the variables

-a^2*3-5a*3-14=0

Wy multiply elements

-3a^2-15a-14=0

a = -3; b = -15; c = -14;
Δ = b2-4ac
Δ = -152-4·(-3)·(-14)
Δ = 57
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{-(-15)-\sqrt{57}}{2*-3}=\frac{15-\sqrt{57}}{-6}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{57}}{2*-3}=\frac{15+\sqrt{57}}{-6}
$