10x+24x-x^2=120

Solution for 10x+24x-x^2=120 equation:

10x+24x-x^2=120

We move all terms to the left:

10x+24x-x^2-(120)=0

We add all the numbers together, and all the variables

-1x^2+34x-120=0

a = -1; b = 34; c = -120;
Δ = b2-4ac
Δ = 342-4·(-1)·(-120)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-26}{2*-1}=\frac{-60}{-2}
=+30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+26}{2*-1}=\frac{-8}{-2}
=+4
$