7x-18=-21/4x+15

Solution for 7x-18=-21/4x+15 equation:

7x-18=-21/4x+15

We move all terms to the left:

7x-18-(-21/4x+15)=0


Domain of the equation: 4x+15)!=0

x∈R


We get rid of parentheses

7x+21/4x-15-18=0

We multiply all the terms by the denominator


7x*4x-15*4x-18*4x+21=0

Wy multiply elements

28x^2-60x-72x+21=0

We add all the numbers together, and all the variables

28x^2-132x+21=0

a = 28; b = -132; c = +21;
Δ = b2-4ac
Δ = -1322-4·28·21
Δ = 15072
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:

$\sqrt{\Delta}=\sqrt{15072}=\sqrt{16*942}=\sqrt{16}*\sqrt{942}=4\sqrt{942}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-132)-4\sqrt{942}}{2*28}=\frac{132-4\sqrt{942}}{56}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-132)+4\sqrt{942}}{2*28}=\frac{132+4\sqrt{942}}{56}
$