8x^2+100X-553=0

Solution for 8x^2+100X-553=0 equation:

8x^2+100x-553=0

a = 8; b = 100; c = -553;
Δ = b2-4ac
Δ = 1002-4·8·(-553)
Δ = 27696
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:

$\sqrt{\Delta}=\sqrt{27696}=\sqrt{16*1731}=\sqrt{16}*\sqrt{1731}=4\sqrt{1731}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-4\sqrt{1731}}{2*8}=\frac{-100-4\sqrt{1731}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+4\sqrt{1731}}{2*8}=\frac{-100+4\sqrt{1731}}{16}
$