7-3(x+5)8x=17

Solution for 7-3(x+5)8x=17 equation:

7-3(x+5)8x=17

We move all terms to the left:

7-3(x+5)8x-(17)=0

We add all the numbers together, and all the variables

-3(x+5)8x-10=0

We multiply parentheses

-24x^2-120x-10=0

a = -24; b = -120; c = -10;
Δ = b2-4ac
Δ = -1202-4·(-24)·(-10)
Δ = 13440
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:

$\sqrt{\Delta}=\sqrt{13440}=\sqrt{64*210}=\sqrt{64}*\sqrt{210}=8\sqrt{210}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-8\sqrt{210}}{2*-24}=\frac{120-8\sqrt{210}}{-48}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+8\sqrt{210}}{2*-24}=\frac{120+8\sqrt{210}}{-48}
$