-6x+15=-7/2x+5

Solution for -6x+15=-7/2x+5 equation:

-6x+15=-7/2x+5

We move all terms to the left:

-6x+15-(-7/2x+5)=0


Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

-6x+7/2x-5+15=0

We multiply all the terms by the denominator


-6x*2x-5*2x+15*2x+7=0

Wy multiply elements

-12x^2-10x+30x+7=0

We add all the numbers together, and all the variables

-12x^2+20x+7=0

a = -12; b = 20; c = +7;
Δ = b2-4ac
Δ = 202-4·(-12)·7
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{46}}{2*-12}=\frac{-20-4\sqrt{46}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{46}}{2*-12}=\frac{-20+4\sqrt{46}}{-24}
$