5x+4=(2/3)(10-x)

Solution for 5x+4=(2/3)(10-x) equation:

5x+4=(2/3)(10-x)

We move all terms to the left:

5x+4-((2/3)(10-x))=0


Domain of the equation: 3)(10-x))!=0

x∈R


We add all the numbers together, and all the variables

5x-((+2/3)(-1x+10))+4=0

We multiply parentheses ..

-((-2x^2+2/3*10))+5x+4=0

We multiply all the terms by the denominator


-((-2x^2+2+5x*3*10))+4*3*10))=0


We calculate terms in parentheses: -((-2x^2+2+5x*3*10)), so:

(-2x^2+2+5x*3*10)

We get rid of parentheses

-2x^2+5x*3*10+2

Wy multiply elements

-2x^2+150x*1+2

Wy multiply elements

-2x^2+150x+2

Back to the equation:

-(-2x^2+150x+2)


We add all the numbers together, and all the variables

-(-2x^2+150x+2)=0

We get rid of parentheses

2x^2-150x-2=0

a = 2; b = -150; c = -2;
Δ = b2-4ac
Δ = -1502-4·2·(-2)
Δ = 22516
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:

$\sqrt{\Delta}=\sqrt{22516}=\sqrt{4*5629}=\sqrt{4}*\sqrt{5629}=2\sqrt{5629}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5629}}{2*2}=\frac{150-2\sqrt{5629}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5629}}{2*2}=\frac{150+2\sqrt{5629}}{4}
$