x+(1/2x-10)=425

Solution for x+(1/2x-10)=425 equation:

x+(1/2x-10)=425

We move all terms to the left:

x+(1/2x-10)-(425)=0


Domain of the equation: 2x-10)!=0

x∈R


We get rid of parentheses

x+1/2x-10-425=0

We multiply all the terms by the denominator


x*2x-10*2x-425*2x+1=0

Wy multiply elements

2x^2-20x-850x+1=0

We add all the numbers together, and all the variables

2x^2-870x+1=0

a = 2; b = -870; c = +1;
Δ = b2-4ac
Δ = -8702-4·2·1
Δ = 756892
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:

$\sqrt{\Delta}=\sqrt{756892}=\sqrt{4*189223}=\sqrt{4}*\sqrt{189223}=2\sqrt{189223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-870)-2\sqrt{189223}}{2*2}=\frac{870-2\sqrt{189223}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-870)+2\sqrt{189223}}{2*2}=\frac{870+2\sqrt{189223}}{4}
$