8(x-5)7x=65

Solution for 8(x-5)7x=65 equation:

8(x-5)7x=65

We move all terms to the left:

8(x-5)7x-(65)=0

We multiply parentheses

56x^2-280x-65=0

a = 56; b = -280; c = -65;
Δ = b2-4ac
Δ = -2802-4·56·(-65)
Δ = 92960
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:

$\sqrt{\Delta}=\sqrt{92960}=\sqrt{16*5810}=\sqrt{16}*\sqrt{5810}=4\sqrt{5810}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-4\sqrt{5810}}{2*56}=\frac{280-4\sqrt{5810}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+4\sqrt{5810}}{2*56}=\frac{280+4\sqrt{5810}}{112}
$