6x+30=(x+5)(x-10)

Solution for 6x+30=(x+5)(x-10) equation:

6x+30=(x+5)(x-10)

We move all terms to the left:

6x+30-((x+5)(x-10))=0

We multiply parentheses ..

-((+x^2-10x+5x-50))+6x+30=0


We calculate terms in parentheses: -((+x^2-10x+5x-50)), so:

(+x^2-10x+5x-50)

We get rid of parentheses

x^2-10x+5x-50

We add all the numbers together, and all the variables

x^2-5x-50

Back to the equation:

-(x^2-5x-50)


We add all the numbers together, and all the variables

6x-(x^2-5x-50)+30=0

We get rid of parentheses

-x^2+6x+5x+50+30=0

We add all the numbers together, and all the variables

-1x^2+11x+80=0

a = -1; b = 11; c = +80;
Δ = b2-4ac
Δ = 112-4·(-1)·80
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-21}{2*-1}=\frac{-32}{-2}
=+16
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+21}{2*-1}=\frac{10}{-2}
=-5
$