8x^2+112x-203=0

Solution for 8x^2+112x-203=0 equation:

8x^2+112x-203=0

a = 8; b = 112; c = -203;
Δ = b2-4ac
Δ = 1122-4·8·(-203)
Δ = 19040
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:

$\sqrt{\Delta}=\sqrt{19040}=\sqrt{16*1190}=\sqrt{16}*\sqrt{1190}=4\sqrt{1190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(112)-4\sqrt{1190}}{2*8}=\frac{-112-4\sqrt{1190}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+4\sqrt{1190}}{2*8}=\frac{-112+4\sqrt{1190}}{16}
$