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4x(6x+3)=10x+5
We move all terms to the left:
4x(6x+3)-(10x+5)=0
We multiply parentheses
24x^2+12x-(10x+5)=0
We get rid of parentheses
24x^2+12x-10x-5=0
We add all the numbers together, and all the variables
24x^2+2x-5=0
a = 24; b = 2; c = -5;
Δ = b2-4ac
Δ = 22-4·24·(-5)
Δ = 484
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{484}=22$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*24}=\frac{-24}{48} =-1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*24}=\frac{20}{48} =5/12 $
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