49x=-x^2

Solution for 49x=-x^2 equation:

49x=-x^2

We move all terms to the left:

49x-(-x^2)=0

We get rid of parentheses

x^2+49x=0

a = 1; b = 49; c = 0;
Δ = b2-4ac
Δ = 492-4·1·0
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(49)-49}{2*1}=\frac{-98}{2}
=-49
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(49)+49}{2*1}=\frac{0}{2}
=0
$