(2x+7)(5x+9)=x

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

(2x+7)(5x+9)=x

We move all terms to the left:

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

We add all the numbers together, and all the variables

-1x+(2x+7)(5x+9)=0

We multiply parentheses ..

(+10x^2+18x+35x+63)-1x=0

We get rid of parentheses

10x^2+18x+35x-1x+63=0

We add all the numbers together, and all the variables

10x^2+52x+63=0

a = 10; b = 52; c = +63;
Δ = b2-4ac
Δ = 522-4·10·63
Δ = 184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-2\sqrt{46}}{2*10}=\frac{-52-2\sqrt{46}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+2\sqrt{46}}{2*10}=\frac{-52+2\sqrt{46}}{20}
$