-42x+18x^2=36

Solution for -42x+18x^2=36 equation:

-42x+18x^2=36

We move all terms to the left:

-42x+18x^2-(36)=0

a = 18; b = -42; c = -36;
Δ = b2-4ac
Δ = -422-4·18·(-36)
Δ = 4356
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4356}=66$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-66}{2*18}=\frac{-24}{36}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+66}{2*18}=\frac{108}{36}
=3
$