16x^2-200x+91=0

Solution for 16x^2-200x+91=0 equation:

16x^2-200x+91=0

a = 16; b = -200; c = +91;
Δ = b2-4ac
Δ = -2002-4·16·91
Δ = 34176
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:

$\sqrt{\Delta}=\sqrt{34176}=\sqrt{64*534}=\sqrt{64}*\sqrt{534}=8\sqrt{534}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-8\sqrt{534}}{2*16}=\frac{200-8\sqrt{534}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+8\sqrt{534}}{2*16}=\frac{200+8\sqrt{534}}{32}
$