3a(4a+9)=4a-10

Solution for 3a(4a+9)=4a-10 equation:

3a(4a+9)=4a-10

We move all terms to the left:

3a(4a+9)-(4a-10)=0

We multiply parentheses

12a^2+27a-(4a-10)=0

We get rid of parentheses

12a^2+27a-4a+10=0

We add all the numbers together, and all the variables

12a^2+23a+10=0

a = 12; b = 23; c = +10;
Δ = b2-4ac
Δ = 232-4·12·10
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-7}{2*12}=\frac{-30}{24}
=-1+1/4
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+7}{2*12}=\frac{-16}{24}
=-2/3
$