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(3x+2)(4x+10)=x
We move all terms to the left:
(3x+2)(4x+10)-(x)=0
We add all the numbers together, and all the variables
-1x+(3x+2)(4x+10)=0
We multiply parentheses ..
(+12x^2+30x+8x+20)-1x=0
We get rid of parentheses
12x^2+30x+8x-1x+20=0
We add all the numbers together, and all the variables
12x^2+37x+20=0
a = 12; b = 37; c = +20;
Δ = b2-4ac
Δ = 372-4·12·20
Δ = 409
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{-(37)-\sqrt{409}}{2*12}=\frac{-37-\sqrt{409}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(37)+\sqrt{409}}{2*12}=\frac{-37+\sqrt{409}}{24} $
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