X+7-4x(x+1)=-10

Solution for X+7-4x(x+1)=-10 equation:

X+7-4X(X+1)=-10

We move all terms to the left:

X+7-4X(X+1)-(-10)=0

We add all the numbers together, and all the variables

X-4X(X+1)+17=0

We multiply parentheses

-4X^2+X-4X+17=0

We add all the numbers together, and all the variables

-4X^2-3X+17=0

a = -4; b = -3; c = +17;
Δ = b2-4ac
Δ = -32-4·(-4)·17
Δ = 281
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{-(-3)-\sqrt{281}}{2*-4}=\frac{3-\sqrt{281}}{-8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{281}}{2*-4}=\frac{3+\sqrt{281}}{-8}
$