4x^2+3x+2=5x+2

Solution for 4x^2+3x+2=5x+2 equation:

4x^2+3x+2=5x+2

We move all terms to the left:

4x^2+3x+2-(5x+2)=0

We get rid of parentheses

4x^2+3x-5x-2+2=0

We add all the numbers together, and all the variables

4x^2-2x=0

a = 4; b = -2; c = 0;
Δ = b2-4ac
Δ = -22-4·4·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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