18x^2-45x+8=0

Solution for 18x^2-45x+8=0 equation:

18x^2-45x+8=0

a = 18; b = -45; c = +8;
Δ = b2-4ac
Δ = -452-4·18·8
Δ = 1449
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:

$\sqrt{\Delta}=\sqrt{1449}=\sqrt{9*161}=\sqrt{9}*\sqrt{161}=3\sqrt{161}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{161}}{2*18}=\frac{45-3\sqrt{161}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{161}}{2*18}=\frac{45+3\sqrt{161}}{36}
$