(x*x)+24x=30

Solution for (x*x)+24x=30 equation:

(x*x)+24x=30

We move all terms to the left:

(x*x)+24x-(30)=0

We add all the numbers together, and all the variables

(+x*x)+24x-30=0

We add all the numbers together, and all the variables

24x+(+x*x)-30=0

We get rid of parentheses

24x+x*x-30=0

Wy multiply elements

x^2+24x-30=0

a = 1; b = 24; c = -30;
Δ = b2-4ac
Δ = 242-4·1·(-30)
Δ = 696
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:

$\sqrt{\Delta}=\sqrt{696}=\sqrt{4*174}=\sqrt{4}*\sqrt{174}=2\sqrt{174}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{174}}{2*1}=\frac{-24-2\sqrt{174}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{174}}{2*1}=\frac{-24+2\sqrt{174}}{2}
$