x+x2/4=189.5

Solution for x+x2/4=189.5 equation:

x+x2/4=189.5

We move all terms to the left:

x+x2/4-(189.5)=0

We add all the numbers together, and all the variables

x+x2/4-189.5=0

We multiply all the terms by the denominator


x*4+x2-(189.5)*4=0

We add all the numbers together, and all the variables

x^2+x*4-758=0

Wy multiply elements

x^2+4x-758=0

a = 1; b = 4; c = -758;
Δ = b2-4ac
Δ = 42-4·1·(-758)
Δ = 3048
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:

$\sqrt{\Delta}=\sqrt{3048}=\sqrt{4*762}=\sqrt{4}*\sqrt{762}=2\sqrt{762}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{762}}{2*1}=\frac{-4-2\sqrt{762}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{762}}{2*1}=\frac{-4+2\sqrt{762}}{2}
$