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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+2x^2+6x-1x-3)=0

We get rid of parentheses

2x^2+6x-1x-3=0

We add all the numbers together, and all the variables

2x^2+5x-3=0

a = 2; b = 5; c = -3;
Δ = b2-4ac
Δ = 52-4·2·(-3)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-7}{2*2}=\frac{-12}{4}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+7}{2*2}=\frac{2}{4}
=1/2
$