4a^2+12a-5=2

Solution for 4a^2+12a-5=2 equation:

4a^2+12a-5=2

We move all terms to the left:

4a^2+12a-5-(2)=0

We add all the numbers together, and all the variables

4a^2+12a-7=0

a = 4; b = 12; c = -7;
Δ = b2-4ac
Δ = 122-4·4·(-7)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-16}{2*4}=\frac{-28}{8}
=-3+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+16}{2*4}=\frac{4}{8}
=1/2
$