7a-4=3(a+9)4a

Solution for 7a-4=3(a+9)4a equation:

7a-4=3(a+9)4a

We move all terms to the left:

7a-4-(3(a+9)4a)=0


We calculate terms in parentheses: -(3(a+9)4a), so:

3(a+9)4a

We multiply parentheses

12a^2+108a

Back to the equation:

-(12a^2+108a)


We get rid of parentheses

-12a^2+7a-108a-4=0

We add all the numbers together, and all the variables

-12a^2-101a-4=0

a = -12; b = -101; c = -4;
Δ = b2-4ac
Δ = -1012-4·(-12)·(-4)
Δ = 10009
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{-(-101)-\sqrt{10009}}{2*-12}=\frac{101-\sqrt{10009}}{-24}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-101)+\sqrt{10009}}{2*-12}=\frac{101+\sqrt{10009}}{-24}
$