(3x+6)(3x+20.4)=(5x-19)(2x-4)

Solution for (3x+6)(3x+20.4)=(5x-19)(2x-4) equation:

(3x+6)(3x+20.4)=(5x-19)(2x-4)

We move all terms to the left:

(3x+6)(3x+20.4)-((5x-19)(2x-4))=0

We multiply parentheses ..

(+9x^2+61.2x+18x+122.4)-((5x-19)(2x-4))=0


We calculate terms in parentheses: -((5x-19)(2x-4)), so:

(5x-19)(2x-4)

We multiply parentheses ..

(+10x^2-20x-38x+76)

We get rid of parentheses

10x^2-20x-38x+76

We add all the numbers together, and all the variables

10x^2-58x+76

Back to the equation:

-(10x^2-58x+76)


We get rid of parentheses

9x^2-10x^2+61.2x+18x+58x+122.4-76=0

We add all the numbers together, and all the variables

-1x^2+137.2x+46.4=0

a = -1; b = 137.2; c = +46.4;
Δ = b2-4ac
Δ = 137.22-4·(-1)·46.4
Δ = 19009.44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(137.2)-\sqrt{19009.44}}{2*-1}=\frac{-137.2-\sqrt{19009.44}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(137.2)+\sqrt{19009.44}}{2*-1}=\frac{-137.2+\sqrt{19009.44}}{-2}
$