7=35/2*2x-20x

Solution for 7=35/2*2x-20x equation:

7=35/2*2x-20x

We move all terms to the left:

7-(35/2*2x-20x)=0


Domain of the equation: 2*2x-20x)!=0

x∈R


We add all the numbers together, and all the variables

-(-20x+35/2*2x)+7=0

We get rid of parentheses

20x-35/2*2x+7=0

We multiply all the terms by the denominator


20x*2*2x+7*2*2x-35=0

Wy multiply elements

80x^2*2+28x*2-35=0

Wy multiply elements

160x^2+56x-35=0

a = 160; b = 56; c = -35;
Δ = b2-4ac
Δ = 562-4·160·(-35)
Δ = 25536
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:

$\sqrt{\Delta}=\sqrt{25536}=\sqrt{64*399}=\sqrt{64}*\sqrt{399}=8\sqrt{399}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-8\sqrt{399}}{2*160}=\frac{-56-8\sqrt{399}}{320}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+8\sqrt{399}}{2*160}=\frac{-56+8\sqrt{399}}{320}
$