x^2-2x-7/16=0

Solution for x^2-2x-7/16=0 equation:

x^2-2x-7/16=0

We multiply all the terms by the denominator


x^2*16-2x*16-7=0

Wy multiply elements

16x^2-32x-7=0

a = 16; b = -32; c = -7;
Δ = b2-4ac
Δ = -322-4·16·(-7)
Δ = 1472
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:

$\sqrt{\Delta}=\sqrt{1472}=\sqrt{64*23}=\sqrt{64}*\sqrt{23}=8\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{23}}{2*16}=\frac{32-8\sqrt{23}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{23}}{2*16}=\frac{32+8\sqrt{23}}{32}
$