4x+6=(3+x)5x

Solution for 4x+6=(3+x)5x equation:

4x+6=(3+x)5x

We move all terms to the left:

4x+6-((3+x)5x)=0

We add all the numbers together, and all the variables

4x-((x+3)5x)+6=0


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

(x+3)5x

We multiply parentheses

5x^2+15x

Back to the equation:

-(5x^2+15x)


We get rid of parentheses

-5x^2+4x-15x+6=0

We add all the numbers together, and all the variables

-5x^2-11x+6=0

a = -5; b = -11; c = +6;
Δ = b2-4ac
Δ = -112-4·(-5)·6
Δ = 241
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{-(-11)-\sqrt{241}}{2*-5}=\frac{11-\sqrt{241}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{241}}{2*-5}=\frac{11+\sqrt{241}}{-10}
$