2(a-5)(a-5)=21a

Solution for 2(a-5)(a-5)=21a equation:

2(a-5)(a-5)=21a

We move all terms to the left:

2(a-5)(a-5)-(21a)=0

We add all the numbers together, and all the variables

-21a+2(a-5)(a-5)=0

We multiply parentheses ..

2(+a^2-5a-5a+25)-21a=0

We multiply parentheses

2a^2-10a-10a-21a+50=0

We add all the numbers together, and all the variables

2a^2-41a+50=0

a = 2; b = -41; c = +50;
Δ = b2-4ac
Δ = -412-4·2·50
Δ = 1281
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-\sqrt{1281}}{2*2}=\frac{41-\sqrt{1281}}{4}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+\sqrt{1281}}{2*2}=\frac{41+\sqrt{1281}}{4}
$