5x^2-12x+8=5

Solution for 5x^2-12x+8=5 equation:

5x^2-12x+8=5

We move all terms to the left:

5x^2-12x+8-(5)=0

We add all the numbers together, and all the variables

5x^2-12x+3=0

a = 5; b = -12; c = +3;
Δ = b2-4ac
Δ = -122-4·5·3
Δ = 84
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:

$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{21}}{2*5}=\frac{12-2\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{21}}{2*5}=\frac{12+2\sqrt{21}}{10}
$