5x^2-7x+2=9

Solution for 5x^2-7x+2=9 equation:

5x^2-7x+2=9

We move all terms to the left:

5x^2-7x+2-(9)=0

We add all the numbers together, and all the variables

5x^2-7x-7=0

a = 5; b = -7; c = -7;
Δ = b2-4ac
Δ = -72-4·5·(-7)
Δ = 189
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:

$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-3\sqrt{21}}{2*5}=\frac{7-3\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+3\sqrt{21}}{2*5}=\frac{7+3\sqrt{21}}{10}
$