x^2+9/16-100=0

Solution for x^2+9/16-100=0 equation:

x^2+9/16-100=0

We multiply all the terms by the denominator


x^2*16+9-100*16=0

We add all the numbers together, and all the variables

x^2*16-1591=0

Wy multiply elements

16x^2-1591=0

a = 16; b = 0; c = -1591;
Δ = b2-4ac
Δ = 02-4·16·(-1591)
Δ = 101824
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:

$\sqrt{\Delta}=\sqrt{101824}=\sqrt{64*1591}=\sqrt{64}*\sqrt{1591}=8\sqrt{1591}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{1591}}{2*16}=\frac{0-8\sqrt{1591}}{32}
=-\frac{8\sqrt{1591}}{32}
=-\frac{\sqrt{1591}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{1591}}{2*16}=\frac{0+8\sqrt{1591}}{32}
=\frac{8\sqrt{1591}}{32}
=\frac{\sqrt{1591}}{4}
$