x^2+3x^2+1,5x-0,5=1,5x+3.5

Solution for x^2+3x^2+1,5x-0,5=1,5x+3.5 equation:

x^2+3x^2+1.5x-0.5=1.5x+3.5

We move all terms to the left:

x^2+3x^2+1.5x-0.5-(1.5x+3.5)=0

We add all the numbers together, and all the variables

4x^2+1.5x-(1.5x+3.5)-0.5=0

We get rid of parentheses

4x^2+1.5x-1.5x-3.5-0.5=0

We add all the numbers together, and all the variables

4x^2-4=0

a = 4; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·4·(-4)
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8}{2*4}=\frac{-8}{8}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8}{2*4}=\frac{8}{8}
=1
$