69/16=x^2

Solution for 69/16=x^2 equation:

69/16=x^2

We move all terms to the left:

69/16-(x^2)=0

We add all the numbers together, and all the variables

-1x^2+69/16=0

We multiply all the terms by the denominator


-1x^2*16+69=0

Wy multiply elements

-16x^2+69=0

a = -16; b = 0; c = +69;
Δ = b2-4ac
Δ = 02-4·(-16)·69
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{69}}{2*-16}=\frac{0-8\sqrt{69}}{-32}
=-\frac{8\sqrt{69}}{-32}
=-\frac{\sqrt{69}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{69}}{2*-16}=\frac{0+8\sqrt{69}}{-32}
=\frac{8\sqrt{69}}{-32}
=\frac{\sqrt{69}}{-4}
$