x(x+19)=37

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Solution for x(x+19)=37 equation: 



x(x+19)=37

We move all terms to the left:

x(x+19)-(37)=0

We multiply parentheses

x^2+19x-37=0

a = 1; b = 19; c = -37;
Δ = b2-4ac
Δ = 192-4·1·(-37)
Δ = 509
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{-(19)-\sqrt{509}}{2*1}=\frac{-19-\sqrt{509}}{2}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{509}}{2*1}=\frac{-19+\sqrt{509}}{2}
$

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