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3/4x+20=26x-16
We move all terms to the left:
3/4x+20-(26x-16)=0
Domain of the equation: 4x!=0We get rid of parentheses
x!=0/4
x!=0
x∈R
3/4x-26x+16+20=0
We multiply all the terms by the denominator
-26x*4x+16*4x+20*4x+3=0
Wy multiply elements
-104x^2+64x+80x+3=0
We add all the numbers together, and all the variables
-104x^2+144x+3=0
a = -104; b = 144; c = +3;
Δ = b2-4ac
Δ = 1442-4·(-104)·3
Δ = 21984
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{21984}=\sqrt{16*1374}=\sqrt{16}*\sqrt{1374}=4\sqrt{1374}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-4\sqrt{1374}}{2*-104}=\frac{-144-4\sqrt{1374}}{-208} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+4\sqrt{1374}}{2*-104}=\frac{-144+4\sqrt{1374}}{-208} $
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