6a^2-8a-25=-3

Solution for 6a^2-8a-25=-3 equation:

6a^2-8a-25=-3

We move all terms to the left:

6a^2-8a-25-(-3)=0

We add all the numbers together, and all the variables

6a^2-8a-22=0

a = 6; b = -8; c = -22;
Δ = b2-4ac
Δ = -82-4·6·(-22)
Δ = 592
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{37}}{2*6}=\frac{8-4\sqrt{37}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{37}}{2*6}=\frac{8+4\sqrt{37}}{12}
$