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(3x+5)(4x+1)=-5
We move all terms to the left:
(3x+5)(4x+1)-(-5)=0
We add all the numbers together, and all the variables
(3x+5)(4x+1)+5=0
We multiply parentheses ..
(+12x^2+3x+20x+5)+5=0
We get rid of parentheses
12x^2+3x+20x+5+5=0
We add all the numbers together, and all the variables
12x^2+23x+10=0
a = 12; b = 23; c = +10;
Δ = b2-4ac
Δ = 232-4·12·10
Δ = 49
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-7}{2*12}=\frac{-30}{24} =-1+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+7}{2*12}=\frac{-16}{24} =-2/3 $
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