7+(4+x)=3-(2x-14)x

Solution for 7+(4+x)=3-(2x-14)x equation:

7+(4+x)=3-(2x-14)x

We move all terms to the left:

7+(4+x)-(3-(2x-14)x)=0

We add all the numbers together, and all the variables

(x+4)-(3-(2x-14)x)+7=0

We get rid of parentheses

x-(3-(2x-14)x)+4+7=0


We calculate terms in parentheses: -(3-(2x-14)x), so:

3-(2x-14)x

determiningTheFunctionDomain
-(2x-14)x+3

We multiply parentheses

-2x^2+14x+3

Back to the equation:

-(-2x^2+14x+3)


We add all the numbers together, and all the variables

-(-2x^2+14x+3)+x+11=0

We get rid of parentheses

2x^2-14x+x-3+11=0

We add all the numbers together, and all the variables

2x^2-13x+8=0

a = 2; b = -13; c = +8;
Δ = b2-4ac
Δ = -132-4·2·8
Δ = 105
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{-(-13)-\sqrt{105}}{2*2}=\frac{13-\sqrt{105}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{105}}{2*2}=\frac{13+\sqrt{105}}{4}
$