(3x+2)(2x+7)=0

Solution for (3x+2)(2x+7)=0 equation:

(3x+2)(2x+7)=0

We multiply parentheses ..

(+6x^2+21x+4x+14)=0

We get rid of parentheses

6x^2+21x+4x+14=0

We add all the numbers together, and all the variables

6x^2+25x+14=0

a = 6; b = 25; c = +14;
Δ = b2-4ac
Δ = 252-4·6·14
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{-(25)-17}{2*6}=\frac{-42}{12}
=-3+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+17}{2*6}=\frac{-8}{12}
=-2/3
$