4x^2-5x=x^2-31x+9

Solution for 4x^2-5x=x^2-31x+9 equation:

4x^2-5x=x^2-31x+9

We move all terms to the left:

4x^2-5x-(x^2-31x+9)=0

We get rid of parentheses

4x^2-x^2-5x+31x-9=0

We add all the numbers together, and all the variables

3x^2+26x-9=0

a = 3; b = 26; c = -9;
Δ = b2-4ac
Δ = 262-4·3·(-9)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-28}{2*3}=\frac{-54}{6}
=-9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+28}{2*3}=\frac{2}{6}
=1/3
$