6a^2-12a-25=-7

Solution for 6a^2-12a-25=-7 equation:

6a^2-12a-25=-7

We move all terms to the left:

6a^2-12a-25-(-7)=0

We add all the numbers together, and all the variables

6a^2-12a-18=0

a = 6; b = -12; c = -18;
Δ = b2-4ac
Δ = -122-4·6·(-18)
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-24}{2*6}=\frac{-12}{12}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+24}{2*6}=\frac{36}{12}
=3
$