5(3x+7)=20-2x(x+1)

Solution for 5(3x+7)=20-2x(x+1) equation:

5(3x+7)=20-2x(x+1)

We move all terms to the left:

5(3x+7)-(20-2x(x+1))=0

We multiply parentheses

15x-(20-2x(x+1))+35=0


We calculate terms in parentheses: -(20-2x(x+1)), so:

20-2x(x+1)

determiningTheFunctionDomain
-2x(x+1)+20

We multiply parentheses

-2x^2-2x+20

Back to the equation:

-(-2x^2-2x+20)


We get rid of parentheses

2x^2+2x+15x-20+35=0

We add all the numbers together, and all the variables

2x^2+17x+15=0

a = 2; b = 17; c = +15;
Δ = b2-4ac
Δ = 172-4·2·15
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{-(17)-13}{2*2}=\frac{-30}{4}
=-7+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+13}{2*2}=\frac{-4}{4}
=-1
$