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(12+2x)(x)=310
We move all terms to the left:
(12+2x)(x)-(310)=0
We add all the numbers together, and all the variables
(2x+12)x-310=0
We multiply parentheses
2x^2+12x-310=0
a = 2; b = 12; c = -310;
Δ = b2-4ac
Δ = 122-4·2·(-310)
Δ = 2624
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2624}=\sqrt{64*41}=\sqrt{64}*\sqrt{41}=8\sqrt{41}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-8\sqrt{41}}{2*2}=\frac{-12-8\sqrt{41}}{4} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+8\sqrt{41}}{2*2}=\frac{-12+8\sqrt{41}}{4} $
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