7(x2)=5(x+4)

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

7(x2)=5(x+4)

We move all terms to the left:

7(x2)-(5(x+4))=0

We add all the numbers together, and all the variables

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


We calculate terms in parentheses: -(5(x+4)), so:

5(x+4)

We multiply parentheses

5x+20

Back to the equation:

-(5x+20)


We get rid of 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}
$