5x(2)+3=3(x+7)

Solution for 5x(2)+3=3(x+7) equation:

5x(2)+3=3(x+7)

We move all terms to the left:

5x(2)+3-(3(x+7))=0

We add all the numbers together, and all the variables

5x^2-(3(x+7))+3=0


We calculate terms in parentheses: -(3(x+7)), so:

3(x+7)

We multiply parentheses

3x+21

Back to the equation:

-(3x+21)


We get rid of parentheses

5x^2-3x-21+3=0

We add all the numbers together, and all the variables

5x^2-3x-18=0

a = 5; b = -3; c = -18;
Δ = b2-4ac
Δ = -32-4·5·(-18)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{41}}{2*5}=\frac{3-3\sqrt{41}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{41}}{2*5}=\frac{3+3\sqrt{41}}{10}
$