x(x+7)=35

Solution for x(x+7)=35 equation:

x(x+7)=35

We move all terms to the left:

x(x+7)-(35)=0

We multiply parentheses

x^2+7x-35=0

a = 1; b = 7; c = -35;
Δ = b2-4ac
Δ = 72-4·1·(-35)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{21}}{2*1}=\frac{-7-3\sqrt{21}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{21}}{2*1}=\frac{-7+3\sqrt{21}}{2}
$