4x^2-x=2x^2+7x

Solution for 4x^2-x=2x^2+7x equation:

4x^2-x=2x^2+7x

We move all terms to the left:

4x^2-x-(2x^2+7x)=0

We add all the numbers together, and all the variables

4x^2-1x-(2x^2+7x)=0

We get rid of parentheses

4x^2-2x^2-1x-7x=0

We add all the numbers together, and all the variables

2x^2-8x=0

a = 2; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·2·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*2}=\frac{16}{4}
=4
$