X=6x-7/2x+5

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

X=6X-7/2X+5

We move all terms to the left:

X-(6X-7/2X+5)=0


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

X∈R


We get rid of parentheses

X-6X+7/2X-5=0

We multiply all the terms by the denominator


X*2X-6X*2X-5*2X+7=0

Wy multiply elements

2X^2-12X^2-10X+7=0

We add all the numbers together, and all the variables

-10X^2-10X+7=0

a = -10; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·(-10)·7
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{95}}{2*-10}=\frac{10-2\sqrt{95}}{-20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{95}}{2*-10}=\frac{10+2\sqrt{95}}{-20}
$