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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+3x^2+18x-10x-60))=0


We calculate terms in parentheses: -((+3x^2+18x-10x-60)), so:

(+3x^2+18x-10x-60)

We get rid of parentheses

3x^2+18x-10x-60

We add all the numbers together, and all the variables

3x^2+8x-60

Back to the equation:

-(3x^2+8x-60)


We get rid of parentheses

-3x^2-8x+60=0

a = -3; b = -8; c = +60;
Δ = b2-4ac
Δ = -82-4·(-3)·60
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-28}{2*-3}=\frac{-20}{-6}
=3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+28}{2*-3}=\frac{36}{-6}
=-6
$