8x2+192x+1170=7225

Solution for 8x2+192x+1170=7225 equation:

8x^2+192x+1170=7225

We move all terms to the left:

8x^2+192x+1170-(7225)=0

We add all the numbers together, and all the variables

8x^2+192x-6055=0

a = 8; b = 192; c = -6055;
Δ = b2-4ac
Δ = 1922-4·8·(-6055)
Δ = 230624
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:

$\sqrt{\Delta}=\sqrt{230624}=\sqrt{16*14414}=\sqrt{16}*\sqrt{14414}=4\sqrt{14414}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(192)-4\sqrt{14414}}{2*8}=\frac{-192-4\sqrt{14414}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(192)+4\sqrt{14414}}{2*8}=\frac{-192+4\sqrt{14414}}{16}
$