5x+5=3(5x-4)10x

Solution for 5x+5=3(5x-4)10x equation:

5x+5=3(5x-4)10x

We move all terms to the left:

5x+5-(3(5x-4)10x)=0


We calculate terms in parentheses: -(3(5x-4)10x), so:

3(5x-4)10x

We multiply parentheses

150x^2-120x

Back to the equation:

-(150x^2-120x)


We get rid of parentheses

-150x^2+5x+120x+5=0

We add all the numbers together, and all the variables

-150x^2+125x+5=0

a = -150; b = 125; c = +5;
Δ = b2-4ac
Δ = 1252-4·(-150)·5
Δ = 18625
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:

$\sqrt{\Delta}=\sqrt{18625}=\sqrt{25*745}=\sqrt{25}*\sqrt{745}=5\sqrt{745}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(125)-5\sqrt{745}}{2*-150}=\frac{-125-5\sqrt{745}}{-300}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(125)+5\sqrt{745}}{2*-150}=\frac{-125+5\sqrt{745}}{-300}
$