3x2+0.5=7.5x

Solution for 3x2+0.5=7.5x equation:

3x^2+0.5=7.5x

We move all terms to the left:

3x^2+0.5-(7.5x)=0

We add all the numbers together, and all the variables

3x^2-(+7.5x)+0.5=0

We get rid of parentheses

3x^2-7.5x+0.5=0

a = 3; b = -7.5; c = +0.5;
Δ = b2-4ac
Δ = -7.52-4·3·0.5
Δ = 50.25
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{-(-7.5)-\sqrt{50.25}}{2*3}=\frac{7.5-\sqrt{50.25}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7.5)+\sqrt{50.25}}{2*3}=\frac{7.5+\sqrt{50.25}}{6}
$