5x+x^2/2=180

Solution for 5x+x^2/2=180 equation:

5x+x^2/2=180

We move all terms to the left:

5x+x^2/2-(180)=0

We multiply all the terms by the denominator


x^2+5x*2-180*2=0

We add all the numbers together, and all the variables

x^2+5x*2-360=0

Wy multiply elements

x^2+10x-360=0

a = 1; b = 10; c = -360;
Δ = b2-4ac
Δ = 102-4·1·(-360)
Δ = 1540
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:

$\sqrt{\Delta}=\sqrt{1540}=\sqrt{4*385}=\sqrt{4}*\sqrt{385}=2\sqrt{385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{385}}{2*1}=\frac{-10-2\sqrt{385}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{385}}{2*1}=\frac{-10+2\sqrt{385}}{2}
$