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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+13x+6=0

a = 2; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·2·6
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-11}{2*2}=\frac{-24}{4}
=-6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+11}{2*2}=\frac{-2}{4}
=-1/2
$