71x-6.25=x^2

Solution for 71x-6.25=x^2 equation:

71x-6.25=x^2

We move all terms to the left:

71x-6.25-(x^2)=0

determiningTheFunctionDomain
-x^2+71x-6.25=0

We add all the numbers together, and all the variables

-1x^2+71x-6.25=0

a = -1; b = 71; c = -6.25;
Δ = b2-4ac
Δ = 712-4·(-1)·(-6.25)
Δ = 5016
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:

$\sqrt{\Delta}=\sqrt{5016}=\sqrt{4*1254}=\sqrt{4}*\sqrt{1254}=2\sqrt{1254}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(71)-2\sqrt{1254}}{2*-1}=\frac{-71-2\sqrt{1254}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(71)+2\sqrt{1254}}{2*-1}=\frac{-71+2\sqrt{1254}}{-2}
$