(3x-10)(5x+30)=x

Solution for (3x-10)(5x+30)=x equation:

(3x-10)(5x+30)=x

We move all terms to the left:

(3x-10)(5x+30)-(x)=0

We add all the numbers together, and all the variables

-1x+(3x-10)(5x+30)=0

We multiply parentheses ..

(+15x^2+90x-50x-300)-1x=0

We get rid of parentheses

15x^2+90x-50x-1x-300=0

We add all the numbers together, and all the variables

15x^2+39x-300=0

a = 15; b = 39; c = -300;
Δ = b2-4ac
Δ = 392-4·15·(-300)
Δ = 19521
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:

$\sqrt{\Delta}=\sqrt{19521}=\sqrt{81*241}=\sqrt{81}*\sqrt{241}=9\sqrt{241}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-9\sqrt{241}}{2*15}=\frac{-39-9\sqrt{241}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+9\sqrt{241}}{2*15}=\frac{-39+9\sqrt{241}}{30}
$