32x^2-78x=2

Solution for 32x^2-78x=2 equation:

32x^2-78x=2

We move all terms to the left:

32x^2-78x-(2)=0

a = 32; b = -78; c = -2;
Δ = b2-4ac
Δ = -782-4·32·(-2)
Δ = 6340
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:

$\sqrt{\Delta}=\sqrt{6340}=\sqrt{4*1585}=\sqrt{4}*\sqrt{1585}=2\sqrt{1585}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-2\sqrt{1585}}{2*32}=\frac{78-2\sqrt{1585}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+2\sqrt{1585}}{2*32}=\frac{78+2\sqrt{1585}}{64}
$