3-2x^2=7x

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

3-2x^2=7x

We move all terms to the left:

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

a = -2; b = -7; c = +3;
Δ = b2-4ac
Δ = -72-4·(-2)·3
Δ = 73
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)-\sqrt{73}}{2*-2}=\frac{7-\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{73}}{2*-2}=\frac{7+\sqrt{73}}{-4}
$