(x+58)(x+138)=110

Solution for (x+58)(x+138)=110 equation:

(x+58)(x+138)=110

We move all terms to the left:

(x+58)(x+138)-(110)=0

We multiply parentheses ..

(+x^2+138x+58x+8004)-110=0

We get rid of parentheses

x^2+138x+58x+8004-110=0

We add all the numbers together, and all the variables

x^2+196x+7894=0

a = 1; b = 196; c = +7894;
Δ = b2-4ac
Δ = 1962-4·1·7894
Δ = 6840
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{6840}=\sqrt{36*190}=\sqrt{36}*\sqrt{190}=6\sqrt{190}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(196)-6\sqrt{190}}{2*1}=\frac{-196-6\sqrt{190}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(196)+6\sqrt{190}}{2*1}=\frac{-196+6\sqrt{190}}{2}
$