90-1/2x+15=2x-50

Solution for 90-1/2x+15=2x-50 equation:

90-1/2x+15=2x-50

We move all terms to the left:

90-1/2x+15-(2x-50)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1/2x-(2x-50)+105=0

We get rid of parentheses

-1/2x-2x+50+105=0

We multiply all the terms by the denominator


-2x*2x+50*2x+105*2x-1=0

Wy multiply elements

-4x^2+100x+210x-1=0

We add all the numbers together, and all the variables

-4x^2+310x-1=0

a = -4; b = 310; c = -1;
Δ = b2-4ac
Δ = 3102-4·(-4)·(-1)
Δ = 96084
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:

$\sqrt{\Delta}=\sqrt{96084}=\sqrt{36*2669}=\sqrt{36}*\sqrt{2669}=6\sqrt{2669}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(310)-6\sqrt{2669}}{2*-4}=\frac{-310-6\sqrt{2669}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(310)+6\sqrt{2669}}{2*-4}=\frac{-310+6\sqrt{2669}}{-8}
$