(8+X)x=43

Solution for (8+X)x=43 equation:

(8+X)X=43

We move all terms to the left:

(8+X)X-(43)=0

We add all the numbers together, and all the variables

(X+8)X-43=0

We multiply parentheses

X^2+8X-43=0

a = 1; b = 8; c = -43;
Δ = b2-4ac
Δ = 82-4·1·(-43)
Δ = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{59}}{2*1}=\frac{-8-2\sqrt{59}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{59}}{2*1}=\frac{-8+2\sqrt{59}}{2}
$