(5x+3)(6x+4)=0

Solution for (5x+3)(6x+4)=0 equation:

(5x+3)(6x+4)=0

We multiply parentheses ..

(+30x^2+20x+18x+12)=0

We get rid of parentheses

30x^2+20x+18x+12=0

We add all the numbers together, and all the variables

30x^2+38x+12=0

a = 30; b = 38; c = +12;
Δ = b2-4ac
Δ = 382-4·30·12
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2}{2*30}=\frac{-40}{60}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2}{2*30}=\frac{-36}{60}
=-3/5
$