(3x-17)(2x-5)=113

Solution for (3x-17)(2x-5)=113 equation:

(3x-17)(2x-5)=113

We move all terms to the left:

(3x-17)(2x-5)-(113)=0

We multiply parentheses ..

(+6x^2-15x-34x+85)-113=0

We get rid of parentheses

6x^2-15x-34x+85-113=0

We add all the numbers together, and all the variables

6x^2-49x-28=0

a = 6; b = -49; c = -28;
Δ = b2-4ac
Δ = -492-4·6·(-28)
Δ = 3073
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{-(-49)-\sqrt{3073}}{2*6}=\frac{49-\sqrt{3073}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+\sqrt{3073}}{2*6}=\frac{49+\sqrt{3073}}{12}
$