2.5x(x-3)+1.7x=10.8(x+1.5)

Solution for 2.5x(x-3)+1.7x=10.8(x+1.5) equation:

2.5x(x-3)+1.7x=10.8(x+1.5)

We move all terms to the left:

2.5x(x-3)+1.7x-(10.8(x+1.5))=0

We add all the numbers together, and all the variables

1.7x+2.5x(x-3)-(10.8(x+1.5))=0

We multiply parentheses

2x^2+1.7x-6x-(10.8(x+1.5))=0


We calculate terms in parentheses: -(10.8(x+1.5)), so:

10.8(x+1.5)

We multiply parentheses

10.8x+16.2

Back to the equation:

-(10.8x+16.2)


We add all the numbers together, and all the variables

2x^2-4.3x-(10.8x+16.2)=0

We get rid of parentheses

2x^2-4.3x-10.8x-16.2=0

We add all the numbers together, and all the variables

2x^2-15.1x-16.2=0

a = 2; b = -15.1; c = -16.2;
Δ = b2-4ac
Δ = -15.12-4·2·(-16.2)
Δ = 357.61
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{-(-15.1)-\sqrt{357.61}}{2*2}=\frac{15.1-\sqrt{357.61}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15.1)+\sqrt{357.61}}{2*2}=\frac{15.1+\sqrt{357.61}}{4}
$