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

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

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

We move all terms to the left:

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


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses

3x^2-(2x+30)+14.5=0

We get rid of parentheses

3x^2-2x-30+14.5=0

We add all the numbers together, and all the variables

3x^2-2x-15.5=0

a = 3; b = -2; c = -15.5;
Δ = b2-4ac
Δ = -22-4·3·(-15.5)
Δ = 190
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{-(-2)-\sqrt{190}}{2*3}=\frac{2-\sqrt{190}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{190}}{2*3}=\frac{2+\sqrt{190}}{6}
$