(2x-5)(7x-17)=85

Solution for (2x-5)(7x-17)=85 equation:

(2x-5)(7x-17)=85

We move all terms to the left:

(2x-5)(7x-17)-(85)=0

We multiply parentheses ..

(+14x^2-34x-35x+85)-85=0

We get rid of parentheses

14x^2-34x-35x+85-85=0

We add all the numbers together, and all the variables

14x^2-69x=0

a = 14; b = -69; c = 0;
Δ = b2-4ac
Δ = -692-4·14·0
Δ = 4761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4761}=69$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-69}{2*14}=\frac{0}{28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+69}{2*14}=\frac{138}{28}
=4+13/14
$