6x^2+4.5x=5292

Solution for 6x^2+4.5x=5292 equation:

6x^2+4.5x=5292

We move all terms to the left:

6x^2+4.5x-(5292)=0

a = 6; b = 4.5; c = -5292;
Δ = b2-4ac
Δ = 4.52-4·6·(-5292)
Δ = 127028.25
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{-(4.5)-\sqrt{127028.25}}{2*6}=\frac{-4.5-\sqrt{127028.25}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4.5)+\sqrt{127028.25}}{2*6}=\frac{-4.5+\sqrt{127028.25}}{12}
$