3a^2-51a=5a^2-25-6a

Solution for 3a^2-51a=5a^2-25-6a equation:

3a^2-51a=5a^2-25-6a

We move all terms to the left:

3a^2-51a-(5a^2-25-6a)=0

We get rid of parentheses

3a^2-5a^2-51a+6a+25=0

We add all the numbers together, and all the variables

-2a^2-45a+25=0

a = -2; b = -45; c = +25;
Δ = b2-4ac
Δ = -452-4·(-2)·25
Δ = 2225
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:

$\sqrt{\Delta}=\sqrt{2225}=\sqrt{25*89}=\sqrt{25}*\sqrt{89}=5\sqrt{89}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-5\sqrt{89}}{2*-2}=\frac{45-5\sqrt{89}}{-4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+5\sqrt{89}}{2*-2}=\frac{45+5\sqrt{89}}{-4}
$