3x+4-2x=3/5x+7

Solution for 3x+4-2x=3/5x+7 equation:

3x+4-2x=3/5x+7

We move all terms to the left:

3x+4-2x-(3/5x+7)=0


Domain of the equation: 5x+7)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

5x^2-35x+20x-3=0

We add all the numbers together, and all the variables

5x^2-15x-3=0

a = 5; b = -15; c = -3;
Δ = b2-4ac
Δ = -152-4·5·(-3)
Δ = 285
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{285}}{2*5}=\frac{15-\sqrt{285}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+\sqrt{285}}{2*5}=\frac{15+\sqrt{285}}{10}
$