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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(2(x+5)), so:

2(x+5)

We multiply parentheses

2x+10

Back to the equation:

-(2x+10)


We get rid of parentheses

x^2-3x-2x-10=0

We add all the numbers together, and all the variables

x^2-5x-10=0

a = 1; b = -5; c = -10;
Δ = b2-4ac
Δ = -52-4·1·(-10)
Δ = 65
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{-(-5)-\sqrt{65}}{2*1}=\frac{5-\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*1}=\frac{5+\sqrt{65}}{2}
$