(2x-10)(3x-4)=0

Solution for (2x-10)(3x-4)=0 equation:

(2x-10)(3x-4)=0

We multiply parentheses ..

(+6x^2-8x-30x+40)=0

We get rid of parentheses

6x^2-8x-30x+40=0

We add all the numbers together, and all the variables

6x^2-38x+40=0

a = 6; b = -38; c = +40;
Δ = b2-4ac
Δ = -382-4·6·40
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-22}{2*6}=\frac{16}{12}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+22}{2*6}=\frac{60}{12}
=5
$