7x^2+5=2x+9

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

7x^2+5=2x+9

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

7x^2-2x-4=0

a = 7; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·7·(-4)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{29}}{2*7}=\frac{2-2\sqrt{29}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{29}}{2*7}=\frac{2+2\sqrt{29}}{14}
$