Explanation:
the area of a triangle is
length × width
in our case
(x + 10) × x = 50
x² + 10x = 50
x² + 10x - 50 = 0
the general solution to such a quadratic equation
ax² + bx + c = 0
is
x = (-b ± sqrt(b² - 4ac))/(2a)
in our case that is
x = (-10 ± sqrt(10² - 4×1×-50))/(2×1) =
= (-10 ± sqrt(100 + 200))/2 =
= (-10 ± sqrt(300))/2 = (-10 ± sqrt(100×3))/2 =
= -5 ± sqrt(100×3/4) = -5 ± sqrt(25×3) =
= -5 ± 5×sqrt(3)
x1 = -5 + 5×sqrt(3) = 3.660254038...
x2 = -5 - 5×sqrt(3) = -13.66025404...
x2 gives us negative values for length and width. that does not make any sense for actual lengths of objects.
so,
x = 3.660254038...