4x^2+5x=x+3

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

4x^2+5x=x+3

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2+4x-3=0

a = 4; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·4·(-3)
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{-(4)-8}{2*4}=\frac{-12}{8}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*4}=\frac{4}{8}
=1/2
$