7x^2+64x-143=-43

Solution for 7x^2+64x-143=-43 equation:

7x^2+64x-143=-43

We move all terms to the left:

7x^2+64x-143-(-43)=0

We add all the numbers together, and all the variables

7x^2+64x-100=0

a = 7; b = 64; c = -100;
Δ = b2-4ac
Δ = 642-4·7·(-100)
Δ = 6896
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:

$\sqrt{\Delta}=\sqrt{6896}=\sqrt{16*431}=\sqrt{16}*\sqrt{431}=4\sqrt{431}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{431}}{2*7}=\frac{-64-4\sqrt{431}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{431}}{2*7}=\frac{-64+4\sqrt{431}}{14}
$