x^2-3.5x+5/16=0

Solution for x^2-3.5x+5/16=0 equation:

x^2-3.5x+5/16=0

We multiply all the terms by the denominator


x^2*16-(3.5x)*16+5=0

We add all the numbers together, and all the variables

x^2*16-(+3.5x)*16+5=0

We multiply parentheses

x^2*16-48x+5=0

Wy multiply elements

16x^2-48x+5=0

a = 16; b = -48; c = +5;
Δ = b2-4ac
Δ = -482-4·16·5
Δ = 1984
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:

$\sqrt{\Delta}=\sqrt{1984}=\sqrt{64*31}=\sqrt{64}*\sqrt{31}=8\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{31}}{2*16}=\frac{48-8\sqrt{31}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{31}}{2*16}=\frac{48+8\sqrt{31}}{32}
$