5x(x-7)=2(x+14)

Solution for 5x(x-7)=2(x+14) equation:

5x(x-7)=2(x+14)

We move all terms to the left:

5x(x-7)-(2(x+14))=0

We multiply parentheses

5x^2-35x-(2(x+14))=0


We calculate terms in parentheses: -(2(x+14)), so:

2(x+14)

We multiply parentheses

2x+28

Back to the equation:

-(2x+28)


We get rid of parentheses

5x^2-35x-2x-28=0

We add all the numbers together, and all the variables

5x^2-37x-28=0

a = 5; b = -37; c = -28;
Δ = b2-4ac
Δ = -372-4·5·(-28)
Δ = 1929
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{-(-37)-\sqrt{1929}}{2*5}=\frac{37-\sqrt{1929}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-37)+\sqrt{1929}}{2*5}=\frac{37+\sqrt{1929}}{10}
$