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-5x(3x+4)-6(3+5x-3+4)=10x
We move all terms to the left:
-5x(3x+4)-6(3+5x-3+4)-(10x)=0
We add all the numbers together, and all the variables
-5x(3x+4)-6(5x+4)-10x=0
We add all the numbers together, and all the variables
-10x-5x(3x+4)-6(5x+4)=0
We multiply parentheses
-15x^2-10x-20x-30x-24=0
We add all the numbers together, and all the variables
-15x^2-60x-24=0
a = -15; b = -60; c = -24;
Δ = b2-4ac
Δ = -602-4·(-15)·(-24)
Δ = 2160
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2160}=\sqrt{144*15}=\sqrt{144}*\sqrt{15}=12\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-12\sqrt{15}}{2*-15}=\frac{60-12\sqrt{15}}{-30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+12\sqrt{15}}{2*-15}=\frac{60+12\sqrt{15}}{-30} $
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