(7x-5)(2x-9)=35

Solution for (7x-5)(2x-9)=35 equation:

(7x-5)(2x-9)=35

We move all terms to the left:

(7x-5)(2x-9)-(35)=0

We multiply parentheses ..

(+14x^2-63x-10x+45)-35=0

We get rid of parentheses

14x^2-63x-10x+45-35=0

We add all the numbers together, and all the variables

14x^2-73x+10=0

a = 14; b = -73; c = +10;
Δ = b2-4ac
Δ = -732-4·14·10
Δ = 4769
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-73)-\sqrt{4769}}{2*14}=\frac{73-\sqrt{4769}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-73)+\sqrt{4769}}{2*14}=\frac{73+\sqrt{4769}}{28}
$