98x-49=2^3-x^2

Solution for 98x-49=2^3-x^2 equation:

98x-49=2^3-x^2

We move all terms to the left:

98x-49-(2^3-x^2)=0

We get rid of parentheses

x^2+98x-49-2^3=0

We add all the numbers together, and all the variables

x^2+98x-57=0

a = 1; b = 98; c = -57;
Δ = b2-4ac
Δ = 982-4·1·(-57)
Δ = 9832
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{9832}=\sqrt{4*2458}=\sqrt{4}*\sqrt{2458}=2\sqrt{2458}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-2\sqrt{2458}}{2*1}=\frac{-98-2\sqrt{2458}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+2\sqrt{2458}}{2*1}=\frac{-98+2\sqrt{2458}}{2}
$