7x(x-9)=49

Solution for 7x(x-9)=49 equation:

7x(x-9)=49

We move all terms to the left:

7x(x-9)-(49)=0

We multiply parentheses

7x^2-63x-49=0

a = 7; b = -63; c = -49;
Δ = b2-4ac
Δ = -632-4·7·(-49)
Δ = 5341
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:

$\sqrt{\Delta}=\sqrt{5341}=\sqrt{49*109}=\sqrt{49}*\sqrt{109}=7\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-7\sqrt{109}}{2*7}=\frac{63-7\sqrt{109}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+7\sqrt{109}}{2*7}=\frac{63+7\sqrt{109}}{14}
$