4x(2x-9)=-2(5x-6)

Solution for 4x(2x-9)=-2(5x-6) equation:

4x(2x-9)=-2(5x-6)

We move all terms to the left:

4x(2x-9)-(-2(5x-6))=0

We multiply parentheses

8x^2-36x-(-2(5x-6))=0


We calculate terms in parentheses: -(-2(5x-6)), so:

-2(5x-6)

We multiply parentheses

-10x+12

Back to the equation:

-(-10x+12)


We get rid of parentheses

8x^2-36x+10x-12=0

We add all the numbers together, and all the variables

8x^2-26x-12=0

a = 8; b = -26; c = -12;
Δ = b2-4ac
Δ = -262-4·8·(-12)
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{265}}{2*8}=\frac{26-2\sqrt{265}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{265}}{2*8}=\frac{26+2\sqrt{265}}{16}
$