(x)=-3x^2+72x+25

Solution for (x)=-3x^2+72x+25 equation:

(x)=-3x^2+72x+25

We move all terms to the left:

(x)-(-3x^2+72x+25)=0

We get rid of parentheses

3x^2-72x+x-25=0

We add all the numbers together, and all the variables

3x^2-71x-25=0

a = 3; b = -71; c = -25;
Δ = b2-4ac
Δ = -712-4·3·(-25)
Δ = 5341
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{5341}=\sqrt{49*109}=\sqrt{49}*\sqrt{109}=7\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-71)-7\sqrt{109}}{2*3}=\frac{71-7\sqrt{109}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-71)+7\sqrt{109}}{2*3}=\frac{71+7\sqrt{109}}{6}
$