0=2x^2+38x+140

Solution for 0=2x^2+38x+140 equation:

0=2x^2+38x+140

We move all terms to the left:

0-(2x^2+38x+140)=0

We add all the numbers together, and all the variables

-(2x^2+38x+140)=0

We get rid of parentheses

-2x^2-38x-140=0

a = -2; b = -38; c = -140;
Δ = b2-4ac
Δ = -382-4·(-2)·(-140)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-18}{2*-2}=\frac{20}{-4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+18}{2*-2}=\frac{56}{-4}
=-14
$