8x^2-48x-42=0

Solution for 8x^2-48x-42=0 equation:

8x^2-48x-42=0

a = 8; b = -48; c = -42;
Δ = b2-4ac
Δ = -482-4·8·(-42)
Δ = 3648
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:

$\sqrt{\Delta}=\sqrt{3648}=\sqrt{64*57}=\sqrt{64}*\sqrt{57}=8\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-8\sqrt{57}}{2*8}=\frac{48-8\sqrt{57}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+8\sqrt{57}}{2*8}=\frac{48+8\sqrt{57}}{16}
$