7x2-16x=8

Solution for 7x2-16x=8 equation:

7x^2-16x=8

We move all terms to the left:

7x^2-16x-(8)=0

a = 7; b = -16; c = -8;
Δ = b2-4ac
Δ = -162-4·7·(-8)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{30}}{2*7}=\frac{16-4\sqrt{30}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{30}}{2*7}=\frac{16+4\sqrt{30}}{14}
$