7x(2x-9)=0

Solution for 7x(2x-9)=0 equation:

7x(2x-9)=0

We multiply parentheses

14x^2-63x=0

a = 14; b = -63; c = 0;
Δ = b2-4ac
Δ = -632-4·14·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-63}{2*14}=\frac{0}{28}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+63}{2*14}=\frac{126}{28}
=4+1/2
$