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3-4x(2+3x)=1+5x
We move all terms to the left:
3-4x(2+3x)-(1+5x)=0
We add all the numbers together, and all the variables
-4x(3x+2)-(5x+1)+3=0
We multiply parentheses
-12x^2-8x-(5x+1)+3=0
We get rid of parentheses
-12x^2-8x-5x-1+3=0
We add all the numbers together, and all the variables
-12x^2-13x+2=0
a = -12; b = -13; c = +2;
Δ = b2-4ac
Δ = -132-4·(-12)·2
Δ = 265
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{265}}{2*-12}=\frac{13-\sqrt{265}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{265}}{2*-12}=\frac{13+\sqrt{265}}{-24} $
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