16x^2-84x+49=0

Solution for 16x^2-84x+49=0 equation:

16x^2-84x+49=0

a = 16; b = -84; c = +49;
Δ = b2-4ac
Δ = -842-4·16·49
Δ = 3920
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:

$\sqrt{\Delta}=\sqrt{3920}=\sqrt{784*5}=\sqrt{784}*\sqrt{5}=28\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-28\sqrt{5}}{2*16}=\frac{84-28\sqrt{5}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+28\sqrt{5}}{2*16}=\frac{84+28\sqrt{5}}{32}
$