64+x^2=144,x

Solution for 64+x^2=144,x equation:

64+x^2=144.x

We move all terms to the left:

64+x^2-(144.x)=0

We add all the numbers together, and all the variables

x^2-(+144.x)+64=0

We get rid of parentheses

x^2-144.x+64=0

We add all the numbers together, and all the variables

x^2-144x+64=0

a = 1; b = -144; c = +64;
Δ = b2-4ac
Δ = -1442-4·1·64
Δ = 20480
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{20480}=\sqrt{4096*5}=\sqrt{4096}*\sqrt{5}=64\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-64\sqrt{5}}{2*1}=\frac{144-64\sqrt{5}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+64\sqrt{5}}{2*1}=\frac{144+64\sqrt{5}}{2}
$