x(x+7)=114

Solution for x(x+7)=114 equation:

x(x+7)=114

We move all terms to the left:

x(x+7)-(114)=0

We multiply parentheses

x^2+7x-114=0

a = 1; b = 7; c = -114;
Δ = b2-4ac
Δ = 72-4·1·(-114)
Δ = 505
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{-(7)-\sqrt{505}}{2*1}=\frac{-7-\sqrt{505}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{505}}{2*1}=\frac{-7+\sqrt{505}}{2}
$