7x2=14+3x

Solution for 7x2=14+3x equation:

7x^2=14+3x

We move all terms to the left:

7x^2-(14+3x)=0

We add all the numbers together, and all the variables

7x^2-(3x+14)=0

We get rid of parentheses

7x^2-3x-14=0

a = 7; b = -3; c = -14;
Δ = b2-4ac
Δ = -32-4·7·(-14)
Δ = 401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{401}}{2*7}=\frac{3-\sqrt{401}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{401}}{2*7}=\frac{3+\sqrt{401}}{14}
$