x^2=91(x+7)

Solution for x^2=91(x+7) equation:

x^2=91(x+7)

We move all terms to the left:

x^2-(91(x+7))=0


We calculate terms in parentheses: -(91(x+7)), so:

91(x+7)

We multiply parentheses

91x+637

Back to the equation:

-(91x+637)


We get rid of parentheses

x^2-91x-637=0

a = 1; b = -91; c = -637;
Δ = b2-4ac
Δ = -912-4·1·(-637)
Δ = 10829
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:

$\sqrt{\Delta}=\sqrt{10829}=\sqrt{49*221}=\sqrt{49}*\sqrt{221}=7\sqrt{221}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-91)-7\sqrt{221}}{2*1}=\frac{91-7\sqrt{221}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-91)+7\sqrt{221}}{2*1}=\frac{91+7\sqrt{221}}{2}
$