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-1/4x-3+2x-6+90=180

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Solution for -1/4x-3+2x-6+90=180 equation:



-1/4x-3+2x-6+90=180
We move all terms to the left:
-1/4x-3+2x-6+90-(180)=0
Domain of the equation: 4x!=0
x!=0/4
x!=0
x∈R
We add all the numbers together, and all the variables
2x-1/4x-99=0
We multiply all the terms by the denominator
2x*4x-99*4x-1=0
Wy multiply elements
8x^2-396x-1=0
a = 8; b = -396; c = -1;
Δ = b2-4ac
Δ = -3962-4·8·(-1)
Δ = 156848
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{156848}=\sqrt{16*9803}=\sqrt{16}*\sqrt{9803}=4\sqrt{9803}
x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-396)-4\sqrt{9803}}{2*8}=\frac{396-4\sqrt{9803}}{16}
x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-396)+4\sqrt{9803}}{2*8}=\frac{396+4\sqrt{9803}}{16}

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