2x-7/20(2x)=x+90

Solution for 2x-7/20(2x)=x+90 equation:

2x-7/20(2x)=x+90

We move all terms to the left:

2x-7/20(2x)-(x+90)=0


Domain of the equation: 202x!=0

x!=0/202

x!=0

x∈R


We get rid of parentheses

2x-7/202x-x-90=0

We multiply all the terms by the denominator


2x*202x-x*202x-90*202x-7=0

Wy multiply elements

404x^2-202x^2-18180x-7=0

We add all the numbers together, and all the variables

202x^2-18180x-7=0

a = 202; b = -18180; c = -7;
Δ = b2-4ac
Δ = -181802-4·202·(-7)
Δ = 330518056
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:

$\sqrt{\Delta}=\sqrt{330518056}=\sqrt{4*82629514}=\sqrt{4}*\sqrt{82629514}=2\sqrt{82629514}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18180)-2\sqrt{82629514}}{2*202}=\frac{18180-2\sqrt{82629514}}{404}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18180)+2\sqrt{82629514}}{2*202}=\frac{18180+2\sqrt{82629514}}{404}
$