7x^2-45=4x

Solution for 7x^2-45=4x equation:

7x^2-45=4x

We move all terms to the left:

7x^2-45-(4x)=0

a = 7; b = -4; c = -45;
Δ = b2-4ac
Δ = -42-4·7·(-45)
Δ = 1276
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:

$\sqrt{\Delta}=\sqrt{1276}=\sqrt{4*319}=\sqrt{4}*\sqrt{319}=2\sqrt{319}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{319}}{2*7}=\frac{4-2\sqrt{319}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{319}}{2*7}=\frac{4+2\sqrt{319}}{14}
$