5=7x2+4x

Solution for 5=7x2+4x equation:

5=7x^2+4x

We move all terms to the left:

5-(7x^2+4x)=0

We get rid of parentheses

-7x^2-4x+5=0

a = -7; b = -4; c = +5;
Δ = b2-4ac
Δ = -42-4·(-7)·5
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{39}}{2*-7}=\frac{4-2\sqrt{39}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{39}}{2*-7}=\frac{4+2\sqrt{39}}{-14}
$