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3x=-4(5-4x)+3/3
We move all terms to the left:
3x-(-4(5-4x)+3/3)=0
We add all the numbers together, and all the variables
3x-(-4(-4x+5)+3/3)=0
We multiply all the terms by the denominator
3x*3)-(-4(-4x+5)+3=0
We multiply parentheses
3x*3)-(+16x-20+3=0
Wy multiply elements
9x^2+16x-20+3=0
We add all the numbers together, and all the variables
9x^2+16x-17=0
a = 9; b = 16; c = -17;
Δ = b2-4ac
Δ = 162-4·9·(-17)
Δ = 868
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{217}}{2*9}=\frac{-16-2\sqrt{217}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{217}}{2*9}=\frac{-16+2\sqrt{217}}{18} $
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