-23x=2/3x+10

Solution for -23x=2/3x+10 equation:

-23x=2/3x+10

We move all terms to the left:

-23x-(2/3x+10)=0


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

x∈R


We get rid of parentheses

-23x-2/3x-10=0

We multiply all the terms by the denominator


-23x*3x-10*3x-2=0

Wy multiply elements

-69x^2-30x-2=0

a = -69; b = -30; c = -2;
Δ = b2-4ac
Δ = -302-4·(-69)·(-2)
Δ = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{87}}{2*-69}=\frac{30-2\sqrt{87}}{-138}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{87}}{2*-69}=\frac{30+2\sqrt{87}}{-138}
$