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7x-18=-21/4x+15
We move all terms to the left:
7x-18-(-21/4x+15)=0
Domain of the equation: 4x+15)!=0We get rid of parentheses
x∈R
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} $
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