a2/3=a+19

Solution for a2/3=a+19 equation:

a2/3=a+19

We move all terms to the left:

a2/3-(a+19)=0

We get rid of parentheses

a2/3-a-19=0

We multiply all the terms by the denominator


a2-a*3-19*3=0

We add all the numbers together, and all the variables

a^2-a*3-57=0

Wy multiply elements

a^2-3a-57=0

a = 1; b = -3; c = -57;
Δ = b2-4ac
Δ = -32-4·1·(-57)
Δ = 237
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{237}}{2*1}=\frac{3-\sqrt{237}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{237}}{2*1}=\frac{3+\sqrt{237}}{2}
$