5x2-49x+249=8x2-82x+239

Solution for 5x2-49x+249=8x2-82x+239 equation:

5x^2-49x+249=8x^2-82x+239

We move all terms to the left:

5x^2-49x+249-(8x^2-82x+239)=0

We get rid of parentheses

5x^2-8x^2-49x+82x-239+249=0

We add all the numbers together, and all the variables

-3x^2+33x+10=0

a = -3; b = 33; c = +10;
Δ = b2-4ac
Δ = 332-4·(-3)·10
Δ = 1209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-\sqrt{1209}}{2*-3}=\frac{-33-\sqrt{1209}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{1209}}{2*-3}=\frac{-33+\sqrt{1209}}{-6}
$