10x^2-4x=16

Solution for 10x^2-4x=16 equation:

10x^2-4x=16

We move all terms to the left:

10x^2-4x-(16)=0

a = 10; b = -4; c = -16;
Δ = b2-4ac
Δ = -42-4·10·(-16)
Δ = 656
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:

$\sqrt{\Delta}=\sqrt{656}=\sqrt{16*41}=\sqrt{16}*\sqrt{41}=4\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{41}}{2*10}=\frac{4-4\sqrt{41}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{41}}{2*10}=\frac{4+4\sqrt{41}}{20}
$