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

Solution for (2x-5)(x-3x)=0 equation:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-4x^2+10x)=0

We get rid of parentheses

-4x^2+10x=0

a = -4; b = 10; c = 0;
Δ = b2-4ac
Δ = 102-4·(-4)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10}{2*-4}=\frac{-20}{-8}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10}{2*-4}=\frac{0}{-8}
=0
$