90x-27-42x^2=0

Solution for 90x-27-42x^2=0 equation:

90x-27-42x^2=0

a = -42; b = 90; c = -27;
Δ = b2-4ac
Δ = 902-4·(-42)·(-27)
Δ = 3564
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:

$\sqrt{\Delta}=\sqrt{3564}=\sqrt{324*11}=\sqrt{324}*\sqrt{11}=18\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-18\sqrt{11}}{2*-42}=\frac{-90-18\sqrt{11}}{-84}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+18\sqrt{11}}{2*-42}=\frac{-90+18\sqrt{11}}{-84}
$