3+4x(7-2x)=-1-(x+5)

Solution for 3+4x(7-2x)=-1-(x+5) equation:

3+4x(7-2x)=-1-(x+5)

We move all terms to the left:

3+4x(7-2x)-(-1-(x+5))=0

We add all the numbers together, and all the variables

4x(-2x+7)-(-1-(x+5))+3=0

We multiply parentheses

-8x^2+28x-(-1-(x+5))+3=0


We calculate terms in parentheses: -(-1-(x+5)), so:

-1-(x+5)

determiningTheFunctionDomain
-(x+5)-1

We get rid of parentheses

-x-5-1

We add all the numbers together, and all the variables

-1x-6

Back to the equation:

-(-1x-6)


We get rid of parentheses

-8x^2+28x+1x+6+3=0

We add all the numbers together, and all the variables

-8x^2+29x+9=0

a = -8; b = 29; c = +9;
Δ = b2-4ac
Δ = 292-4·(-8)·9
Δ = 1129
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-\sqrt{1129}}{2*-8}=\frac{-29-\sqrt{1129}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+\sqrt{1129}}{2*-8}=\frac{-29+\sqrt{1129}}{-16}
$