6x^2-9x=4

Solution for 6x^2-9x=4 equation:

6x^2-9x=4

We move all terms to the left:

6x^2-9x-(4)=0

a = 6; b = -9; c = -4;
Δ = b2-4ac
Δ = -92-4·6·(-4)
Δ = 177
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{-(-9)-\sqrt{177}}{2*6}=\frac{9-\sqrt{177}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{177}}{2*6}=\frac{9+\sqrt{177}}{12}
$