x=25-3x^2

Solution for x=25-3x^2 equation:

x=25-3x^2

We move all terms to the left:

x-(25-3x^2)=0

We get rid of parentheses

3x^2+x-25=0

a = 3; b = 1; c = -25;
Δ = b2-4ac
Δ = 12-4·3·(-25)
Δ = 301
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{-(1)-\sqrt{301}}{2*3}=\frac{-1-\sqrt{301}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{301}}{2*3}=\frac{-1+\sqrt{301}}{6}
$