2x+13=7x2

Solution for 2x+13=7x2 equation:

2x+13=7x^2

We move all terms to the left:

2x+13-(7x^2)=0

determiningTheFunctionDomain
-7x^2+2x+13=0

a = -7; b = 2; c = +13;
Δ = b2-4ac
Δ = 22-4·(-7)·13
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-4\sqrt{23}}{2*-7}=\frac{-2-4\sqrt{23}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+4\sqrt{23}}{2*-7}=\frac{-2+4\sqrt{23}}{-14}
$