x(x+5)=374

Solution for x(x+5)=374 equation:

x(x+5)=374

We move all terms to the left:

x(x+5)-(374)=0

We multiply parentheses

x^2+5x-374=0

a = 1; b = 5; c = -374;
Δ = b2-4ac
Δ = 52-4·1·(-374)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-39}{2*1}=\frac{-44}{2}
=-22
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+39}{2*1}=\frac{34}{2}
=17
$