(4+x)(7+x)=54

Solution for (4+x)(7+x)=54 equation:

(4+x)(7+x)=54

We move all terms to the left:

(4+x)(7+x)-(54)=0

We add all the numbers together, and all the variables

(x+4)(x+7)-54=0

We multiply parentheses ..

(+x^2+7x+4x+28)-54=0

We get rid of parentheses

x^2+7x+4x+28-54=0

We add all the numbers together, and all the variables

x^2+11x-26=0

a = 1; b = 11; c = -26;
Δ = b2-4ac
Δ = 112-4·1·(-26)
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{-(11)-15}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+15}{2*1}=\frac{4}{2}
=2
$