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.50x(4x-6)+3x=5x+3
We move all terms to the left:
.50x(4x-6)+3x-(5x+3)=0
We add all the numbers together, and all the variables
3x+.50x(4x-6)-(5x+3)=0
We multiply parentheses
4x^2+3x-6x-(5x+3)=0
We get rid of parentheses
4x^2+3x-6x-5x-3=0
We add all the numbers together, and all the variables
4x^2-8x-3=0
a = 4; b = -8; c = -3;
Δ = b2-4ac
Δ = -82-4·4·(-3)
Δ = 112
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{7}}{2*4}=\frac{8-4\sqrt{7}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{7}}{2*4}=\frac{8+4\sqrt{7}}{8} $
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