(2x-1)(10-3x)=0

Solution for (2x-1)(10-3x)=0 equation:

(2x-1)(10-3x)=0

We add all the numbers together, and all the variables

(2x-1)(-3x+10)=0

We multiply parentheses ..

(-6x^2+20x+3x-10)=0

We get rid of parentheses

-6x^2+20x+3x-10=0

We add all the numbers together, and all the variables

-6x^2+23x-10=0

a = -6; b = 23; c = -10;
Δ = b2-4ac
Δ = 232-4·(-6)·(-10)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-17}{2*-6}=\frac{-40}{-12}
=3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+17}{2*-6}=\frac{-6}{-12}
=1/2
$