a2+64=100,a

Solution for a2+64=100,a equation:

a2+64=100.a

We move all terms to the left:

a2+64-(100.a)=0

We add all the numbers together, and all the variables

a2-(+100.a)+64=0

We add all the numbers together, and all the variables

a^2-(+100.a)+64=0

We get rid of parentheses

a^2-100.a+64=0

We add all the numbers together, and all the variables

a^2-100a+64=0

a = 1; b = -100; c = +64;
Δ = b2-4ac
Δ = -1002-4·1·64
Δ = 9744
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:

$\sqrt{\Delta}=\sqrt{9744}=\sqrt{16*609}=\sqrt{16}*\sqrt{609}=4\sqrt{609}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-4\sqrt{609}}{2*1}=\frac{100-4\sqrt{609}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+4\sqrt{609}}{2*1}=\frac{100+4\sqrt{609}}{2}
$