5x+69=2x^2-14x-19

Solution for 5x+69=2x^2-14x-19 equation:

5x+69=2x^2-14x-19

We move all terms to the left:

5x+69-(2x^2-14x-19)=0

We get rid of parentheses

-2x^2+5x+14x+19+69=0

We add all the numbers together, and all the variables

-2x^2+19x+88=0

a = -2; b = 19; c = +88;
Δ = b2-4ac
Δ = 192-4·(-2)·88
Δ = 1065
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{-(19)-\sqrt{1065}}{2*-2}=\frac{-19-\sqrt{1065}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{1065}}{2*-2}=\frac{-19+\sqrt{1065}}{-4}
$