12a^2-40a-35=-3

Solution for 12a^2-40a-35=-3 equation:

12a^2-40a-35=-3

We move all terms to the left:

12a^2-40a-35-(-3)=0

We add all the numbers together, and all the variables

12a^2-40a-32=0

a = 12; b = -40; c = -32;
Δ = b2-4ac
Δ = -402-4·12·(-32)
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-56}{2*12}=\frac{-16}{24}
=-2/3
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+56}{2*12}=\frac{96}{24}
=4
$