x(x+49)=50

Solution for x(x+49)=50 equation:

x(x+49)=50

We move all terms to the left:

x(x+49)-(50)=0

We multiply parentheses

x^2+49x-50=0

a = 1; b = 49; c = -50;
Δ = b2-4ac
Δ = 492-4·1·(-50)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-51}{2*1}=\frac{-100}{2}
=-50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+51}{2*1}=\frac{2}{2}
=1
$