16x^2-22x=3

Solution for 16x^2-22x=3 equation:

16x^2-22x=3

We move all terms to the left:

16x^2-22x-(3)=0

a = 16; b = -22; c = -3;
Δ = b2-4ac
Δ = -222-4·16·(-3)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-26}{2*16}=\frac{-4}{32}
=-1/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+26}{2*16}=\frac{48}{32}
=1+1/2
$