8x^2-6x-275=133

Solution for 8x^2-6x-275=133 equation:

8x^2-6x-275=133

We move all terms to the left:

8x^2-6x-275-(133)=0

We add all the numbers together, and all the variables

8x^2-6x-408=0

a = 8; b = -6; c = -408;
Δ = b2-4ac
Δ = -62-4·8·(-408)
Δ = 13092
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:

$\sqrt{\Delta}=\sqrt{13092}=\sqrt{4*3273}=\sqrt{4}*\sqrt{3273}=2\sqrt{3273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{3273}}{2*8}=\frac{6-2\sqrt{3273}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{3273}}{2*8}=\frac{6+2\sqrt{3273}}{16}
$