2.5x-4=3/4x-7

Solution for 2.5x-4=3/4x-7 equation:

2.5x-4=3/4x-7

We move all terms to the left:

2.5x-4-(3/4x-7)=0


Domain of the equation: 4x-7)!=0

x∈R


We get rid of parentheses

2.5x-3/4x+7-4=0

We multiply all the terms by the denominator


(2.5x)*4x+7*4x-4*4x-3=0

We add all the numbers together, and all the variables

(+2.5x)*4x+7*4x-4*4x-3=0

We multiply parentheses

8x^2+7*4x-4*4x-3=0

Wy multiply elements

8x^2+28x-16x-3=0

We add all the numbers together, and all the variables

8x^2+12x-3=0

a = 8; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·8·(-3)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{15}}{2*8}=\frac{-12-4\sqrt{15}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{15}}{2*8}=\frac{-12+4\sqrt{15}}{16}
$