(3x-10)(5x-10)=2x

Solution for (3x-10)(5x-10)=2x equation:

(3x-10)(5x-10)=2x

We move all terms to the left:

(3x-10)(5x-10)-(2x)=0

We add all the numbers together, and all the variables

-2x+(3x-10)(5x-10)=0

We multiply parentheses ..

(+15x^2-30x-50x+100)-2x=0

We get rid of parentheses

15x^2-30x-50x-2x+100=0

We add all the numbers together, and all the variables

15x^2-82x+100=0

a = 15; b = -82; c = +100;
Δ = b2-4ac
Δ = -822-4·15·100
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-82)-2\sqrt{181}}{2*15}=\frac{82-2\sqrt{181}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-82)+2\sqrt{181}}{2*15}=\frac{82+2\sqrt{181}}{30}
$