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

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(-6x^2+10x-9x+15)=0

We get rid of parentheses

-6x^2+10x-9x+15=0

We add all the numbers together, and all the variables

-6x^2+x+15=0

a = -6; b = 1; c = +15;
Δ = b2-4ac
Δ = 12-4·(-6)·15
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-19}{2*-6}=\frac{-20}{-12}
=1+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+19}{2*-6}=\frac{18}{-12}
=-1+1/2
$