4.5+(3/5x)+10=2x+30

Solution for 4.5+(3/5x)+10=2x+30 equation:

4.5+(3/5x)+10=2x+30

We move all terms to the left:

4.5+(3/5x)+10-(2x+30)=0


Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+3/5x)-(2x+30)+4.5+10=0

We add all the numbers together, and all the variables

(+3/5x)-(2x+30)+14.5=0

We get rid of parentheses

3/5x-2x-30+14.5=0

We multiply all the terms by the denominator


-2x*5x-30*5x+(14.5)*5x+3=0

We multiply parentheses

-2x*5x-30*5x+72.5x+3=0

Wy multiply elements

-10x^2-150x+72.5x+3=0

We add all the numbers together, and all the variables

-10x^2-77.5x+3=0

a = -10; b = -77.5; c = +3;
Δ = b2-4ac
Δ = -77.52-4·(-10)·3
Δ = 6126.25
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{-(-77.5)-\sqrt{6126.25}}{2*-10}=\frac{77.5-\sqrt{6126.25}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-77.5)+\sqrt{6126.25}}{2*-10}=\frac{77.5+\sqrt{6126.25}}{-20}
$