5x^2-30x+29=0

Solution for 5x^2-30x+29=0 equation:

5x^2-30x+29=0

a = 5; b = -30; c = +29;
Δ = b2-4ac
Δ = -302-4·5·29
Δ = 320
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:

$\sqrt{\Delta}=\sqrt{320}=\sqrt{64*5}=\sqrt{64}*\sqrt{5}=8\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-8\sqrt{5}}{2*5}=\frac{30-8\sqrt{5}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+8\sqrt{5}}{2*5}=\frac{30+8\sqrt{5}}{10}
$