3x2+2.5=12-5

Solution for 3x2+2.5=12-5 equation:

3x^2+2.5=12-5

We move all terms to the left:

3x^2+2.5-(12-5)=0

We add all the numbers together, and all the variables

3x^2+2.5-7=0

We add all the numbers together, and all the variables

3x^2-4.5=0

a = 3; b = 0; c = -4.5;
Δ = b2-4ac
Δ = 02-4·3·(-4.5)
Δ = 54
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{54}=\sqrt{9*6}=\sqrt{9}*\sqrt{6}=3\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-3\sqrt{6}}{2*3}=\frac{0-3\sqrt{6}}{6}
=-\frac{3\sqrt{6}}{6}
=-\frac{\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+3\sqrt{6}}{2*3}=\frac{0+3\sqrt{6}}{6}
=\frac{3\sqrt{6}}{6}
=\frac{\sqrt{6}}{2}
$