x^2+x/2+3x=7x

Solution for x^2+x/2+3x=7x equation:

x^2+x/2+3x=7x

We move all terms to the left:

x^2+x/2+3x-(7x)=0

We add all the numbers together, and all the variables

x^2-4x+x/2=0

We multiply all the terms by the denominator


x^2*2-4x*2+x=0

We add all the numbers together, and all the variables

x^2*2+x-4x*2=0

Wy multiply elements

2x^2+x-8x=0

We add all the numbers together, and all the variables

2x^2-7x=0

a = 2; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·2·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*2}=\frac{14}{4}
=3+1/2
$