(2x+5)(x-4)=0*

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

(2x+5)(x-4)=0*

We move all terms to the left:

(2x+5)(x-4)-(0*)=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+2x^2-8x+5x-20)=0

We get rid of parentheses

2x^2-8x+5x-20=0

We add all the numbers together, and all the variables

2x^2-3x-20=0

a = 2; b = -3; c = -20;
Δ = b2-4ac
Δ = -32-4·2·(-20)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-13}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+13}{2*2}=\frac{16}{4}
=4
$