25x^2+x=24

Solution for 25x^2+x=24 equation:

25x^2+x=24

We move all terms to the left:

25x^2+x-(24)=0

a = 25; b = 1; c = -24;
Δ = b2-4ac
Δ = 12-4·25·(-24)
Δ = 2401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2401}=49$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-49}{2*25}=\frac{-50}{50}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+49}{2*25}=\frac{48}{50}
=24/25
$