X^2+7x=42^2

Solution for X^2+7x=42^2 equation:

X^2+7X=42^2

We move all terms to the left:

X^2+7X-(42^2)=0

We add all the numbers together, and all the variables

X^2+7X-1764=0

a = 1; b = 7; c = -1764;
Δ = b2-4ac
Δ = 72-4·1·(-1764)
Δ = 7105
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:

$\sqrt{\Delta}=\sqrt{7105}=\sqrt{49*145}=\sqrt{49}*\sqrt{145}=7\sqrt{145}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7\sqrt{145}}{2*1}=\frac{-7-7\sqrt{145}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7\sqrt{145}}{2*1}=\frac{-7+7\sqrt{145}}{2}
$