2x^2-27x+12=-10x-19

Solution for 2x^2-27x+12=-10x-19 equation:

2x^2-27x+12=-10x-19

We move all terms to the left:

2x^2-27x+12-(-10x-19)=0

We get rid of parentheses

2x^2-27x+10x+19+12=0

We add all the numbers together, and all the variables

2x^2-17x+31=0

a = 2; b = -17; c = +31;
Δ = b2-4ac
Δ = -172-4·2·31
Δ = 41
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{-(-17)-\sqrt{41}}{2*2}=\frac{17-\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+\sqrt{41}}{2*2}=\frac{17+\sqrt{41}}{4}
$