X2+6x=59

Solution for X2+6x=59 equation:

X2+6X=59

We move all terms to the left:

X2+6X-(59)=0

We add all the numbers together, and all the variables

X^2+6X-59=0

a = 1; b = 6; c = -59;
Δ = b2-4ac
Δ = 62-4·1·(-59)
Δ = 272
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:

$\sqrt{\Delta}=\sqrt{272}=\sqrt{16*17}=\sqrt{16}*\sqrt{17}=4\sqrt{17}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{17}}{2*1}=\frac{-6-4\sqrt{17}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{17}}{2*1}=\frac{-6+4\sqrt{17}}{2}
$