(10+x)(14+x)=221

Solution for (10+x)(14+x)=221 equation:

(10+x)(14+x)=221

We move all terms to the left:

(10+x)(14+x)-(221)=0

We add all the numbers together, and all the variables

(x+10)(x+14)-221=0

We multiply parentheses ..

(+x^2+14x+10x+140)-221=0

We get rid of parentheses

x^2+14x+10x+140-221=0

We add all the numbers together, and all the variables

x^2+24x-81=0

a = 1; b = 24; c = -81;
Δ = b2-4ac
Δ = 242-4·1·(-81)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-30}{2*1}=\frac{-54}{2}
=-27
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+30}{2*1}=\frac{6}{2}
=3
$