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(3x+7)(4x+5)=x
We move all terms to the left:
(3x+7)(4x+5)-(x)=0
We add all the numbers together, and all the variables
-1x+(3x+7)(4x+5)=0
We multiply parentheses ..
(+12x^2+15x+28x+35)-1x=0
We get rid of parentheses
12x^2+15x+28x-1x+35=0
We add all the numbers together, and all the variables
12x^2+42x+35=0
a = 12; b = 42; c = +35;
Δ = b2-4ac
Δ = 422-4·12·35
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-2\sqrt{21}}{2*12}=\frac{-42-2\sqrt{21}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+2\sqrt{21}}{2*12}=\frac{-42+2\sqrt{21}}{24} $
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