(((5+x)*x)-6)/4=11

Solution for (((5+x)*x)-6)/4=11 equation:

(((5+x)*x)-6)/4=11

We move all terms to the left:

(((5+x)*x)-6)/4-(11)=0

We add all the numbers together, and all the variables

(((x+5)*x)-6)/4-11=0

We multiply all the terms by the denominator


(((x+5)*x)-6)-11*4=0


We calculate terms in parentheses: +(((x+5)*x)-6), so:

((x+5)*x)-6


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

(x+5)*x

We multiply parentheses

x^2+5x

Back to the equation:

+(x^2+5x)


We get rid of parentheses

x^2+5x-6

Back to the equation:

+(x^2+5x-6)


We add all the numbers together, and all the variables

(x^2+5x-6)-44=0

We get rid of parentheses

x^2+5x-6-44=0

We add all the numbers together, and all the variables

x^2+5x-50=0

a = 1; b = 5; c = -50;
Δ = b2-4ac
Δ = 52-4·1·(-50)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-15}{2*1}=\frac{-20}{2}
=-10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+15}{2*1}=\frac{10}{2}
=5
$