x^2/2+35x-62.5=x

Solution for x^2/2+35x-62.5=x equation:

x^2/2+35x-62.5=x

We move all terms to the left:

x^2/2+35x-62.5-(x)=0

We add all the numbers together, and all the variables

x^2/2+34x-62.5=0

We multiply all the terms by the denominator


x^2+34x*2-(62.5)*2=0

We add all the numbers together, and all the variables

x^2+34x*2-125=0

Wy multiply elements

x^2+68x-125=0

a = 1; b = 68; c = -125;
Δ = b2-4ac
Δ = 682-4·1·(-125)
Δ = 5124
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:

$\sqrt{\Delta}=\sqrt{5124}=\sqrt{4*1281}=\sqrt{4}*\sqrt{1281}=2\sqrt{1281}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-2\sqrt{1281}}{2*1}=\frac{-68-2\sqrt{1281}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+2\sqrt{1281}}{2*1}=\frac{-68+2\sqrt{1281}}{2}
$