4x^2+7x=9x+4x

Solution for 4x^2+7x=9x+4x equation:

4x^2+7x=9x+4x

We move all terms to the left:

4x^2+7x-(9x+4x)=0

We add all the numbers together, and all the variables

4x^2+7x-(+13x)=0

We get rid of parentheses

4x^2+7x-13x=0

We add all the numbers together, and all the variables

4x^2-6x=0

a = 4; b = -6; c = 0;
Δ = b2-4ac
Δ = -62-4·4·0
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6}{2*4}=\frac{12}{8}
=1+1/2
$