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8x(3x+5)=-10+6x
We move all terms to the left:
8x(3x+5)-(-10+6x)=0
We add all the numbers together, and all the variables
8x(3x+5)-(6x-10)=0
We multiply parentheses
24x^2+40x-(6x-10)=0
We get rid of parentheses
24x^2+40x-6x+10=0
We add all the numbers together, and all the variables
24x^2+34x+10=0
a = 24; b = 34; c = +10;
Δ = b2-4ac
Δ = 342-4·24·10
Δ = 196
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{196}=14$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-14}{2*24}=\frac{-48}{48} =-1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+14}{2*24}=\frac{-20}{48} =-5/12 $
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