16x^2+28x=4

Solution for 16x^2+28x=4 equation:

16x^2+28x=4

We move all terms to the left:

16x^2+28x-(4)=0

a = 16; b = 28; c = -4;
Δ = b2-4ac
Δ = 282-4·16·(-4)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{65}}{2*16}=\frac{-28-4\sqrt{65}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{65}}{2*16}=\frac{-28+4\sqrt{65}}{32}
$