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8x(3x+10)=15
We move all terms to the left:
8x(3x+10)-(15)=0
We multiply parentheses
24x^2+80x-15=0
a = 24; b = 80; c = -15;
Δ = b2-4ac
Δ = 802-4·24·(-15)
Δ = 7840
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7840}=\sqrt{784*10}=\sqrt{784}*\sqrt{10}=28\sqrt{10}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-28\sqrt{10}}{2*24}=\frac{-80-28\sqrt{10}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+28\sqrt{10}}{2*24}=\frac{-80+28\sqrt{10}}{48} $
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