5(4+x)=7x2

Solution for 5(4+x)=7x2 equation:

5(4+x)=7x^2

We move all terms to the left:

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

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

We add all the numbers together, and all the variables

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

We multiply parentheses

-7x^2+5x+20=0

a = -7; b = 5; c = +20;
Δ = b2-4ac
Δ = 52-4·(-7)·20
Δ = 585
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:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-3\sqrt{65}}{2*-7}=\frac{-5-3\sqrt{65}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+3\sqrt{65}}{2*-7}=\frac{-5+3\sqrt{65}}{-14}
$