7-x(2x+1)=-5

Solution for 7-x(2x+1)=-5 equation:

7-x(2x+1)=-5

We move all terms to the left:

7-x(2x+1)-(-5)=0

We add all the numbers together, and all the variables

-x(2x+1)+12=0

We multiply parentheses

-2x^2-x+12=0

We add all the numbers together, and all the variables

-2x^2-1x+12=0

a = -2; b = -1; c = +12;
Δ = b2-4ac
Δ = -12-4·(-2)·12
Δ = 97
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{97}}{2*-2}=\frac{1-\sqrt{97}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{97}}{2*-2}=\frac{1+\sqrt{97}}{-4}
$