14x^2+33x=-10

Solution for 14x^2+33x=-10 equation:

14x^2+33x=-10

We move all terms to the left:

14x^2+33x-(-10)=0

We add all the numbers together, and all the variables

14x^2+33x+10=0

a = 14; b = 33; c = +10;
Δ = b2-4ac
Δ = 332-4·14·10
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{-(33)-23}{2*14}=\frac{-56}{28}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+23}{2*14}=\frac{-10}{28}
=-5/14
$