5x+24=9x^2-131x+482

Solution for 5x+24=9x^2-131x+482 equation:

5x+24=9x^2-131x+482

We move all terms to the left:

5x+24-(9x^2-131x+482)=0

We get rid of parentheses

-9x^2+5x+131x-482+24=0

We add all the numbers together, and all the variables

-9x^2+136x-458=0

a = -9; b = 136; c = -458;
Δ = b2-4ac
Δ = 1362-4·(-9)·(-458)
Δ = 2008
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:

$\sqrt{\Delta}=\sqrt{2008}=\sqrt{4*502}=\sqrt{4}*\sqrt{502}=2\sqrt{502}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(136)-2\sqrt{502}}{2*-9}=\frac{-136-2\sqrt{502}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(136)+2\sqrt{502}}{2*-9}=\frac{-136+2\sqrt{502}}{-18}
$