5.2x^2-45x+90=0

Solution for 5.2x^2-45x+90=0 equation:

5.2x^2-45x+90=0

a = 5.2; b = -45; c = +90;
Δ = b2-4ac
Δ = -452-4·5.2·90
Δ = 153
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:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-3\sqrt{17}}{2*5.2}=\frac{45-3\sqrt{17}}{10.4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+3\sqrt{17}}{2*5.2}=\frac{45+3\sqrt{17}}{10.4}
$