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(10x-3)(3x+1)=6x
We move all terms to the left:
(10x-3)(3x+1)-(6x)=0
We add all the numbers together, and all the variables
-6x+(10x-3)(3x+1)=0
We multiply parentheses ..
(+30x^2+10x-9x-3)-6x=0
We get rid of parentheses
30x^2+10x-9x-6x-3=0
We add all the numbers together, and all the variables
30x^2-5x-3=0
a = 30; b = -5; c = -3;
Δ = b2-4ac
Δ = -52-4·30·(-3)
Δ = 385
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{-(-5)-\sqrt{385}}{2*30}=\frac{5-\sqrt{385}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{385}}{2*30}=\frac{5+\sqrt{385}}{60} $
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