4x^2-17x=6x+2x^2

Solution for 4x^2-17x=6x+2x^2 equation:

4x^2-17x=6x+2x^2

We move all terms to the left:

4x^2-17x-(6x+2x^2)=0

We get rid of parentheses

4x^2-2x^2-6x-17x=0

We add all the numbers together, and all the variables

2x^2-23x=0

a = 2; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·2·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*2}=\frac{46}{4}
=11+1/2
$