4x=282/7x+5=

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Solution for 4x=282/7x+5= equation: 



4x=282/7x+5=

We move all terms to the left:

4x-(282/7x+5)=0



Domain of the equation: 7x+5)!=0

x∈R



We get rid of parentheses

4x-282/7x-5=0

We multiply all the terms by the denominator


4x*7x-5*7x-282=0

Wy multiply elements

28x^2-35x-282=0

a = 28; b = -35; c = -282;
Δ = b2-4ac
Δ = -352-4·28·(-282)
Δ = 32809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{32809}}{2*28}=\frac{35-\sqrt{32809}}{56}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{32809}}{2*28}=\frac{35+\sqrt{32809}}{56}
$

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