3x^2+31x=4x

Solution for 3x^2+31x=4x equation:

3x^2+31x=4x

We move all terms to the left:

3x^2+31x-(4x)=0

We add all the numbers together, and all the variables

3x^2+27x=0

a = 3; b = 27; c = 0;
Δ = b2-4ac
Δ = 272-4·3·0
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-27}{2*3}=\frac{-54}{6}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+27}{2*3}=\frac{0}{6}
=0
$