16x^2-114x=28

Solution for 16x^2-114x=28 equation:

16x^2-114x=28

We move all terms to the left:

16x^2-114x-(28)=0

a = 16; b = -114; c = -28;
Δ = b2-4ac
Δ = -1142-4·16·(-28)
Δ = 14788
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:

$\sqrt{\Delta}=\sqrt{14788}=\sqrt{4*3697}=\sqrt{4}*\sqrt{3697}=2\sqrt{3697}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-114)-2\sqrt{3697}}{2*16}=\frac{114-2\sqrt{3697}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-114)+2\sqrt{3697}}{2*16}=\frac{114+2\sqrt{3697}}{32}
$