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+6a-51a+25=0

We add all the numbers together, and all the variables

8a^2-45a+25=0

a = 8; b = -45; c = +25;
Δ = b2-4ac
Δ = -452-4·8·25
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-35}{2*8}=\frac{10}{16}
=5/8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+35}{2*8}=\frac{80}{16}
=5
$