7x+20=(3x+3)(5x-10)

Solution for 7x+20=(3x+3)(5x-10) equation:

7x+20=(3x+3)(5x-10)

We move all terms to the left:

7x+20-((3x+3)(5x-10))=0

We multiply parentheses ..

-((+15x^2-30x+15x-30))+7x+20=0


We calculate terms in parentheses: -((+15x^2-30x+15x-30)), so:

(+15x^2-30x+15x-30)

We get rid of parentheses

15x^2-30x+15x-30

We add all the numbers together, and all the variables

15x^2-15x-30

Back to the equation:

-(15x^2-15x-30)


We add all the numbers together, and all the variables

7x-(15x^2-15x-30)+20=0

We get rid of parentheses

-15x^2+7x+15x+30+20=0

We add all the numbers together, and all the variables

-15x^2+22x+50=0

a = -15; b = 22; c = +50;
Δ = b2-4ac
Δ = 222-4·(-15)·50
Δ = 3484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3484}=\sqrt{4*871}=\sqrt{4}*\sqrt{871}=2\sqrt{871}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{871}}{2*-15}=\frac{-22-2\sqrt{871}}{-30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{871}}{2*-15}=\frac{-22+2\sqrt{871}}{-30}
$