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5x-4=7x(3-5x)
We move all terms to the left:
5x-4-(7x(3-5x))=0
We add all the numbers together, and all the variables
5x-(7x(-5x+3))-4=0
We calculate terms in parentheses: -(7x(-5x+3)), so:We get rid of parentheses
7x(-5x+3)
We multiply parentheses
-35x^2+21x
Back to the equation:
-(-35x^2+21x)
35x^2-21x+5x-4=0
We add all the numbers together, and all the variables
35x^2-16x-4=0
a = 35; b = -16; c = -4;
Δ = b2-4ac
Δ = -162-4·35·(-4)
Δ = 816
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{816}=\sqrt{16*51}=\sqrt{16}*\sqrt{51}=4\sqrt{51}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{51}}{2*35}=\frac{16-4\sqrt{51}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{51}}{2*35}=\frac{16+4\sqrt{51}}{70} $
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