5x2=3x+9

Solution for 5x2=3x+9 equation:

5x^2=3x+9

We move all terms to the left:

5x^2-(3x+9)=0

We get rid of parentheses

5x^2-3x-9=0

a = 5; b = -3; c = -9;
Δ = b2-4ac
Δ = -32-4·5·(-9)
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{-(-3)-3\sqrt{21}}{2*5}=\frac{3-3\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{21}}{2*5}=\frac{3+3\sqrt{21}}{10}
$