8x^2-78x=54

Solution for 8x^2-78x=54 equation:

8x^2-78x=54

We move all terms to the left:

8x^2-78x-(54)=0

a = 8; b = -78; c = -54;
Δ = b2-4ac
Δ = -782-4·8·(-54)
Δ = 7812
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:

$\sqrt{\Delta}=\sqrt{7812}=\sqrt{36*217}=\sqrt{36}*\sqrt{217}=6\sqrt{217}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-78)-6\sqrt{217}}{2*8}=\frac{78-6\sqrt{217}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-78)+6\sqrt{217}}{2*8}=\frac{78+6\sqrt{217}}{16}
$