2.5x(6x-4)=10+4(1.5+0.5x)

Solution for 2.5x(6x-4)=10+4(1.5+0.5x) equation:

2.5x(6x-4)=10+4(1.5+0.5x)

We move all terms to the left:

2.5x(6x-4)-(10+4(1.5+0.5x))=0

We add all the numbers together, and all the variables

2.5x(6x-4)-(10+4(0.5x+1.5))=0

We multiply parentheses

12x^2-8x-(10+4(0.5x+1.5))=0


We calculate terms in parentheses: -(10+4(0.5x+1.5)), so:

10+4(0.5x+1.5)

determiningTheFunctionDomain
4(0.5x+1.5)+10

We multiply parentheses

0x+6+10

We add all the numbers together, and all the variables

x+16

Back to the equation:

-(x+16)


We get rid of parentheses

12x^2-8x-x-16=0

We add all the numbers together, and all the variables

12x^2-9x-16=0

a = 12; b = -9; c = -16;
Δ = b2-4ac
Δ = -92-4·12·(-16)
Δ = 849
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{-(-9)-\sqrt{849}}{2*12}=\frac{9-\sqrt{849}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{849}}{2*12}=\frac{9+\sqrt{849}}{24}
$