7x^2-3/2=2x

Solution for 7x^2-3/2=2x equation:

7x^2-3/2=2x

We move all terms to the left:

7x^2-3/2-(2x)=0

We multiply all the terms by the denominator


7x^2*2-2x*2-3=0

Wy multiply elements

14x^2-4x-3=0

a = 14; b = -4; c = -3;
Δ = b2-4ac
Δ = -42-4·14·(-3)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{46}}{2*14}=\frac{4-2\sqrt{46}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{46}}{2*14}=\frac{4+2\sqrt{46}}{28}
$