x+x+x2/4=189.5

Solution for x+x+x2/4=189.5 equation:

x+x+x2/4=189.5

We move all terms to the left:

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

We add all the numbers together, and all the variables

2x+x2/4-189.5=0

We multiply all the terms by the denominator


2x*4+x2-(189.5)*4=0

We add all the numbers together, and all the variables

x^2+2x*4-758=0

Wy multiply elements

x^2+8x-758=0

a = 1; b = 8; c = -758;
Δ = b2-4ac
Δ = 82-4·1·(-758)
Δ = 3096
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:

$\sqrt{\Delta}=\sqrt{3096}=\sqrt{36*86}=\sqrt{36}*\sqrt{86}=6\sqrt{86}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-6\sqrt{86}}{2*1}=\frac{-8-6\sqrt{86}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+6\sqrt{86}}{2*1}=\frac{-8+6\sqrt{86}}{2}
$