(3x+8)(2x+5)=0

Solution for (3x+8)(2x+5)=0 equation:

(3x+8)(2x+5)=0

We multiply parentheses ..

(+6x^2+15x+16x+40)=0

We get rid of parentheses

6x^2+15x+16x+40=0

We add all the numbers together, and all the variables

6x^2+31x+40=0

a = 6; b = 31; c = +40;
Δ = b2-4ac
Δ = 312-4·6·40
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-1}{2*6}=\frac{-32}{12}
=-2+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+1}{2*6}=\frac{-30}{12}
=-2+1/2
$