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

Solution for 4(x-3)(2x-5)=0 equation:

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

We multiply parentheses ..

4(+2x^2-5x-6x+15)=0

We multiply parentheses

8x^2-20x-24x+60=0

We add all the numbers together, and all the variables

8x^2-44x+60=0

a = 8; b = -44; c = +60;
Δ = b2-4ac
Δ = -442-4·8·60
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4}{2*8}=\frac{40}{16}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4}{2*8}=\frac{48}{16}
=3
$