(9-4x)(6-2x)=150

Solution for (9-4x)(6-2x)=150 equation:

(9-4x)(6-2x)=150

We move all terms to the left:

(9-4x)(6-2x)-(150)=0

We add all the numbers together, and all the variables

(-4x+9)(-2x+6)-150=0

We multiply parentheses ..

(+8x^2-24x-18x+54)-150=0

We get rid of parentheses

8x^2-24x-18x+54-150=0

We add all the numbers together, and all the variables

8x^2-42x-96=0

a = 8; b = -42; c = -96;
Δ = b2-4ac
Δ = -422-4·8·(-96)
Δ = 4836
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:

$\sqrt{\Delta}=\sqrt{4836}=\sqrt{4*1209}=\sqrt{4}*\sqrt{1209}=2\sqrt{1209}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{1209}}{2*8}=\frac{42-2\sqrt{1209}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{1209}}{2*8}=\frac{42+2\sqrt{1209}}{16}
$