8x^2+(107-17)x-146=0

Solution for 8x^2+(107-17)x-146=0 equation:

8x^2+(107-17)x-146=0

We add all the numbers together, and all the variables

8x^2+90x-146=0

a = 8; b = 90; c = -146;
Δ = b2-4ac
Δ = 902-4·8·(-146)
Δ = 12772
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:

$\sqrt{\Delta}=\sqrt{12772}=\sqrt{4*3193}=\sqrt{4}*\sqrt{3193}=2\sqrt{3193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-2\sqrt{3193}}{2*8}=\frac{-90-2\sqrt{3193}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+2\sqrt{3193}}{2*8}=\frac{-90+2\sqrt{3193}}{16}
$