4x(x-2)=7x-9

Solution for 4x(x-2)=7x-9 equation:

4x(x-2)=7x-9

We move all terms to the left:

4x(x-2)-(7x-9)=0

We multiply parentheses

4x^2-8x-(7x-9)=0

We get rid of parentheses

4x^2-8x-7x+9=0

We add all the numbers together, and all the variables

4x^2-15x+9=0

a = 4; b = -15; c = +9;
Δ = b2-4ac
Δ = -152-4·4·9
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-9}{2*4}=\frac{6}{8}
=3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+9}{2*4}=\frac{24}{8}
=3
$