15x^2+67x=-2x+50

Solution for 15x^2+67x=-2x+50 equation:

15x^2+67x=-2x+50

We move all terms to the left:

15x^2+67x-(-2x+50)=0

We get rid of parentheses

15x^2+67x+2x-50=0

We add all the numbers together, and all the variables

15x^2+69x-50=0

a = 15; b = 69; c = -50;
Δ = b2-4ac
Δ = 692-4·15·(-50)
Δ = 7761
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(69)-\sqrt{7761}}{2*15}=\frac{-69-\sqrt{7761}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(69)+\sqrt{7761}}{2*15}=\frac{-69+\sqrt{7761}}{30}
$