4x=25-x2

Solution for 4x=25-x2 equation:

4x=25-x2

We move all terms to the left:

4x-(25-x2)=0

We add all the numbers together, and all the variables

-(-1x^2+25)+4x=0

We get rid of parentheses

1x^2+4x-25=0

We add all the numbers together, and all the variables

x^2+4x-25=0

a = 1; b = 4; c = -25;
Δ = b2-4ac
Δ = 42-4·1·(-25)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{29}}{2*1}=\frac{-4-2\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{29}}{2*1}=\frac{-4+2\sqrt{29}}{2}
$