4+5x(7-x)=-1

Solution for 4+5x(7-x)=-1 equation:

4+5x(7-x)=-1

We move all terms to the left:

4+5x(7-x)-(-1)=0

We add all the numbers together, and all the variables

5x(-1x+7)+4-(-1)=0

We add all the numbers together, and all the variables

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

We multiply parentheses

-5x^2+35x+5=0

a = -5; b = 35; c = +5;
Δ = b2-4ac
Δ = 352-4·(-5)·5
Δ = 1325
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1325}=\sqrt{25*53}=\sqrt{25}*\sqrt{53}=5\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-5\sqrt{53}}{2*-5}=\frac{-35-5\sqrt{53}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+5\sqrt{53}}{2*-5}=\frac{-35+5\sqrt{53}}{-10}
$