-4x+15=-7/2x+12

Solution for -4x+15=-7/2x+12 equation:

-4x+15=-7/2x+12

We move all terms to the left:

-4x+15-(-7/2x+12)=0


Domain of the equation: 2x+12)!=0

x∈R


We get rid of parentheses

-4x+7/2x-12+15=0

We multiply all the terms by the denominator


-4x*2x-12*2x+15*2x+7=0

Wy multiply elements

-8x^2-24x+30x+7=0

We add all the numbers together, and all the variables

-8x^2+6x+7=0

a = -8; b = 6; c = +7;
Δ = b2-4ac
Δ = 62-4·(-8)·7
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{65}}{2*-8}=\frac{-6-2\sqrt{65}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{65}}{2*-8}=\frac{-6+2\sqrt{65}}{-16}
$