(3x+50)(6x-10)=0

Solution for (3x+50)(6x-10)=0 equation:

(3x+50)(6x-10)=0

We multiply parentheses ..

(+18x^2-30x+300x-500)=0

We get rid of parentheses

18x^2-30x+300x-500=0

We add all the numbers together, and all the variables

18x^2+270x-500=0

a = 18; b = 270; c = -500;
Δ = b2-4ac
Δ = 2702-4·18·(-500)
Δ = 108900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{108900}=330$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(270)-330}{2*18}=\frac{-600}{36}
=-16+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(270)+330}{2*18}=\frac{60}{36}
=1+2/3
$