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6x(3x+7)=3x+10
We move all terms to the left:
6x(3x+7)-(3x+10)=0
We multiply parentheses
18x^2+42x-(3x+10)=0
We get rid of parentheses
18x^2+42x-3x-10=0
We add all the numbers together, and all the variables
18x^2+39x-10=0
a = 18; b = 39; c = -10;
Δ = b2-4ac
Δ = 392-4·18·(-10)
Δ = 2241
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2241}=\sqrt{9*249}=\sqrt{9}*\sqrt{249}=3\sqrt{249}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{249}}{2*18}=\frac{-39-3\sqrt{249}}{36} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{249}}{2*18}=\frac{-39+3\sqrt{249}}{36} $
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