x(x+35)=114

Solution for x(x+35)=114 equation:

x(x+35)=114

We move all terms to the left:

x(x+35)-(114)=0

We multiply parentheses

x^2+35x-114=0

a = 1; b = 35; c = -114;
Δ = b2-4ac
Δ = 352-4·1·(-114)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-41}{2*1}=\frac{-76}{2}
=-38
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+41}{2*1}=\frac{6}{2}
=3
$