(2x+5)(1-3x)=0

Solution for (2x+5)(1-3x)=0 equation:

(2x+5)(1-3x)=0

We add all the numbers together, and all the variables

(2x+5)(-3x+1)=0

We multiply parentheses ..

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

We get rid of parentheses

-6x^2+2x-15x+5=0

We add all the numbers together, and all the variables

-6x^2-13x+5=0

a = -6; b = -13; c = +5;
Δ = b2-4ac
Δ = -132-4·(-6)·5
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{-(-13)-17}{2*-6}=\frac{-4}{-12}
=1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+17}{2*-6}=\frac{30}{-12}
=-2+1/2
$