3.5x(2x+3)-3x(x+1.5)=1

Solution for 3.5x(2x+3)-3x(x+1.5)=1 equation:

3.5x(2x+3)-3x(x+1.5)=1

We move all terms to the left:

3.5x(2x+3)-3x(x+1.5)-(1)=0

We multiply parentheses

6x^2-3x^2+9x-4.5x-1=0

We add all the numbers together, and all the variables

3x^2+4.5x-1=0

a = 3; b = 4.5; c = -1;
Δ = b2-4ac
Δ = 4.52-4·3·(-1)
Δ = 32.25
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{-(4.5)-\sqrt{32.25}}{2*3}=\frac{-4.5-\sqrt{32.25}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{32.25}}{2*3}=\frac{-4.5+\sqrt{32.25}}{6}
$