9a^2=4+7a

Solution for 9a^2=4+7a equation:

9a^2=4+7a

We move all terms to the left:

9a^2-(4+7a)=0

We add all the numbers together, and all the variables

9a^2-(7a+4)=0

We get rid of parentheses

9a^2-7a-4=0

a = 9; b = -7; c = -4;
Δ = b2-4ac
Δ = -72-4·9·(-4)
Δ = 193
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{-(-7)-\sqrt{193}}{2*9}=\frac{7-\sqrt{193}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{193}}{2*9}=\frac{7+\sqrt{193}}{18}
$