25a^2-144=9

Solution for 25a^2-144=9 equation:

25a^2-144=9

We move all terms to the left:

25a^2-144-(9)=0

We add all the numbers together, and all the variables

25a^2-153=0

a = 25; b = 0; c = -153;
Δ = b2-4ac
Δ = 02-4·25·(-153)
Δ = 15300
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:

$\sqrt{\Delta}=\sqrt{15300}=\sqrt{900*17}=\sqrt{900}*\sqrt{17}=30\sqrt{17}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{17}}{2*25}=\frac{0-30\sqrt{17}}{50}
=-\frac{30\sqrt{17}}{50}
=-\frac{3\sqrt{17}}{5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{17}}{2*25}=\frac{0+30\sqrt{17}}{50}
=\frac{30\sqrt{17}}{50}
=\frac{3\sqrt{17}}{5}
$