5x(11x-5)=85

Solution for 5x(11x-5)=85 equation:

5x(11x-5)=85

We move all terms to the left:

5x(11x-5)-(85)=0

We multiply parentheses

55x^2-25x-85=0

a = 55; b = -25; c = -85;
Δ = b2-4ac
Δ = -252-4·55·(-85)
Δ = 19325
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:

$\sqrt{\Delta}=\sqrt{19325}=\sqrt{25*773}=\sqrt{25}*\sqrt{773}=5\sqrt{773}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{773}}{2*55}=\frac{25-5\sqrt{773}}{110}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{773}}{2*55}=\frac{25+5\sqrt{773}}{110}
$