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4x(x+2)=29-3x
We move all terms to the left:
4x(x+2)-(29-3x)=0
We add all the numbers together, and all the variables
4x(x+2)-(-3x+29)=0
We multiply parentheses
4x^2+8x-(-3x+29)=0
We get rid of parentheses
4x^2+8x+3x-29=0
We add all the numbers together, and all the variables
4x^2+11x-29=0
a = 4; b = 11; c = -29;
Δ = b2-4ac
Δ = 112-4·4·(-29)
Δ = 585
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{65}}{2*4}=\frac{-11-3\sqrt{65}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{65}}{2*4}=\frac{-11+3\sqrt{65}}{8} $
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