6x2+2x/2=7.5

Solution for 6x2+2x/2=7.5 equation:

6x^2+2x/2=7.5

We move all terms to the left:

6x^2+2x/2-(7.5)=0

We add all the numbers together, and all the variables

6x^2+2x/2-7.5=0

We multiply all the terms by the denominator


6x^2*2+2x-(7.5)*2=0

We add all the numbers together, and all the variables

6x^2*2+2x-15=0

Wy multiply elements

12x^2+2x-15=0

a = 12; b = 2; c = -15;
Δ = b2-4ac
Δ = 22-4·12·(-15)
Δ = 724
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:

$\sqrt{\Delta}=\sqrt{724}=\sqrt{4*181}=\sqrt{4}*\sqrt{181}=2\sqrt{181}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{181}}{2*12}=\frac{-2-2\sqrt{181}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{181}}{2*12}=\frac{-2+2\sqrt{181}}{24}
$