(5a)^2/5+12=57

Solution for (5a)^2/5+12=57 equation:

(5a)^2/5+12=57

We move all terms to the left:

(5a)^2/5+12-(57)=0

We add all the numbers together, and all the variables

5a^2/5-45=0

We multiply all the terms by the denominator


5a^2-45*5=0

We add all the numbers together, and all the variables

5a^2-225=0

a = 5; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·5·(-225)
Δ = 4500
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:

$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30\sqrt{5}}{2*5}=\frac{0-30\sqrt{5}}{10}
=-\frac{30\sqrt{5}}{10}
=-3\sqrt{5}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30\sqrt{5}}{2*5}=\frac{0+30\sqrt{5}}{10}
=\frac{30\sqrt{5}}{10}
=3\sqrt{5}
$