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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

-((+x^2+3x-10x-30))=0


We calculate terms in parentheses: -((+x^2+3x-10x-30)), so:

(+x^2+3x-10x-30)

We get rid of parentheses

x^2+3x-10x-30

We add all the numbers together, and all the variables

x^2-7x-30

Back to the equation:

-(x^2-7x-30)


We get rid of parentheses

-x^2+7x+30=0

We add all the numbers together, and all the variables

-1x^2+7x+30=0

a = -1; b = 7; c = +30;
Δ = b2-4ac
Δ = 72-4·(-1)·30
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*-1}=\frac{-20}{-2}
=+10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*-1}=\frac{6}{-2}
=-3
$