7/3x+5=4x+10

Solution for 7/3x+5=4x+10 equation:

7/3x+5=4x+10

We move all terms to the left:

7/3x+5-(4x+10)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

7/3x-4x-10+5=0

We multiply all the terms by the denominator


-4x*3x-10*3x+5*3x+7=0

Wy multiply elements

-12x^2-30x+15x+7=0

We add all the numbers together, and all the variables

-12x^2-15x+7=0

a = -12; b = -15; c = +7;
Δ = b2-4ac
Δ = -152-4·(-12)·7
Δ = 561
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{-(-15)-\sqrt{561}}{2*-12}=\frac{15-\sqrt{561}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{561}}{2*-12}=\frac{15+\sqrt{561}}{-24}
$