7x2+(x-2)=19

Solution for 7x2+(x-2)=19 equation:

7x^2+(x-2)=19

We move all terms to the left:

7x^2+(x-2)-(19)=0

We get rid of parentheses

7x^2+x-2-19=0

We add all the numbers together, and all the variables

7x^2+x-21=0

a = 7; b = 1; c = -21;
Δ = b2-4ac
Δ = 12-4·7·(-21)
Δ = 589
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{-(1)-\sqrt{589}}{2*7}=\frac{-1-\sqrt{589}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{589}}{2*7}=\frac{-1+\sqrt{589}}{14}
$