-2x^2+9x=4

Solution for -2x^2+9x=4 equation:

-2x^2+9x=4

We move all terms to the left:

-2x^2+9x-(4)=0

a = -2; b = 9; c = -4;
Δ = b2-4ac
Δ = 92-4·(-2)·(-4)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-7}{2*-2}=\frac{-16}{-4}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+7}{2*-2}=\frac{-2}{-4}
=1/2
$