(15x+7)(23x-17)=x

Solution for (15x+7)(23x-17)=x equation:

(15x+7)(23x-17)=x

We move all terms to the left:

(15x+7)(23x-17)-(x)=0

We add all the numbers together, and all the variables

-1x+(15x+7)(23x-17)=0

We multiply parentheses ..

(+345x^2-255x+161x-119)-1x=0

We get rid of parentheses

345x^2-255x+161x-1x-119=0

We add all the numbers together, and all the variables

345x^2-95x-119=0

a = 345; b = -95; c = -119;
Δ = b2-4ac
Δ = -952-4·345·(-119)
Δ = 173245
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{-(-95)-\sqrt{173245}}{2*345}=\frac{95-\sqrt{173245}}{690}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-95)+\sqrt{173245}}{2*345}=\frac{95+\sqrt{173245}}{690}
$