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4x(3x+1)=180-23
We move all terms to the left:
4x(3x+1)-(180-23)=0
We add all the numbers together, and all the variables
4x(3x+1)-157=0
We multiply parentheses
12x^2+4x-157=0
a = 12; b = 4; c = -157;
Δ = b2-4ac
Δ = 42-4·12·(-157)
Δ = 7552
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7552}=\sqrt{64*118}=\sqrt{64}*\sqrt{118}=8\sqrt{118}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8\sqrt{118}}{2*12}=\frac{-4-8\sqrt{118}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8\sqrt{118}}{2*12}=\frac{-4+8\sqrt{118}}{24} $
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