x(2x-9)=-7

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

x(2x-9)=-7

We move all terms to the left:

x(2x-9)-(-7)=0

We add all the numbers together, and all the variables

x(2x-9)+7=0

We multiply parentheses

2x^2-9x+7=0

a = 2; b = -9; c = +7;
Δ = b2-4ac
Δ = -92-4·2·7
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-5}{2*2}=\frac{4}{4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+5}{2*2}=\frac{14}{4}
=3+1/2
$