1/2x+1/2x+(x-15)+100(x-25)=540

Solution for 1/2x+1/2x+(x-15)+100(x-25)=540 equation:

1/2x+1/2x+(x-15)+100(x-25)=540

We move all terms to the left:

1/2x+1/2x+(x-15)+100(x-25)-(540)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

1/2x+1/2x+(x-15)+100x-2500-540=0

We get rid of parentheses

1/2x+1/2x+x+100x-15-2500-540=0

We multiply all the terms by the denominator


x*2x+100x*2x-15*2x-2500*2x-540*2x+1+1=0

We add all the numbers together, and all the variables

x*2x+100x*2x-15*2x-2500*2x-540*2x+2=0

Wy multiply elements

2x^2+200x^2-30x-5000x-1080x+2=0

We add all the numbers together, and all the variables

202x^2-6110x+2=0

a = 202; b = -6110; c = +2;
Δ = b2-4ac
Δ = -61102-4·202·2
Δ = 37330484
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:

$\sqrt{\Delta}=\sqrt{37330484}=\sqrt{4*9332621}=\sqrt{4}*\sqrt{9332621}=2\sqrt{9332621}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6110)-2\sqrt{9332621}}{2*202}=\frac{6110-2\sqrt{9332621}}{404}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6110)+2\sqrt{9332621}}{2*202}=\frac{6110+2\sqrt{9332621}}{404}
$