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X=3X-7/4X-7
We move all terms to the left:
X-(3X-7/4X-7)=0
Domain of the equation: 4X-7)!=0We get rid of parentheses
X∈R
X-3X+7/4X+7=0
We multiply all the terms by the denominator
X*4X-3X*4X+7*4X+7=0
Wy multiply elements
4X^2-12X^2+28X+7=0
We add all the numbers together, and all the variables
-8X^2+28X+7=0
a = -8; b = 28; c = +7;
Δ = b2-4ac
Δ = 282-4·(-8)·7
Δ = 1008
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-12\sqrt{7}}{2*-8}=\frac{-28-12\sqrt{7}}{-16} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+12\sqrt{7}}{2*-8}=\frac{-28+12\sqrt{7}}{-16} $
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