24x^2+96x+84=25x^2+125x+150

Solution for 24x^2+96x+84=25x^2+125x+150 equation:

24x^2+96x+84=25x^2+125x+150

We move all terms to the left:

24x^2+96x+84-(25x^2+125x+150)=0

We get rid of parentheses

24x^2-25x^2+96x-125x-150+84=0

We add all the numbers together, and all the variables

-1x^2-29x-66=0

a = -1; b = -29; c = -66;
Δ = b2-4ac
Δ = -292-4·(-1)·(-66)
Δ = 577
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{-(-29)-\sqrt{577}}{2*-1}=\frac{29-\sqrt{577}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+\sqrt{577}}{2*-1}=\frac{29+\sqrt{577}}{-2}
$