(9x+25)(8x+2)=x

Solution for (9x+25)(8x+2)=x equation:

(9x+25)(8x+2)=x

We move all terms to the left:

(9x+25)(8x+2)-(x)=0

We add all the numbers together, and all the variables

-1x+(9x+25)(8x+2)=0

We multiply parentheses ..

(+72x^2+18x+200x+50)-1x=0

We get rid of parentheses

72x^2+18x+200x-1x+50=0

We add all the numbers together, and all the variables

72x^2+217x+50=0

a = 72; b = 217; c = +50;
Δ = b2-4ac
Δ = 2172-4·72·50
Δ = 32689
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{-(217)-\sqrt{32689}}{2*72}=\frac{-217-\sqrt{32689}}{144}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(217)+\sqrt{32689}}{2*72}=\frac{-217+\sqrt{32689}}{144}
$