5(x+3)4x-5=4-2x

Solution for 5(x+3)4x-5=4-2x equation:

5(x+3)4x-5=4-2x

We move all terms to the left:

5(x+3)4x-5-(4-2x)=0

We add all the numbers together, and all the variables

5(x+3)4x-(-2x+4)-5=0

We multiply parentheses

20x^2+60x-(-2x+4)-5=0

We get rid of parentheses

20x^2+60x+2x-4-5=0

We add all the numbers together, and all the variables

20x^2+62x-9=0

a = 20; b = 62; c = -9;
Δ = b2-4ac
Δ = 622-4·20·(-9)
Δ = 4564
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:

$\sqrt{\Delta}=\sqrt{4564}=\sqrt{4*1141}=\sqrt{4}*\sqrt{1141}=2\sqrt{1141}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(62)-2\sqrt{1141}}{2*20}=\frac{-62-2\sqrt{1141}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(62)+2\sqrt{1141}}{2*20}=\frac{-62+2\sqrt{1141}}{40}
$