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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^2-20x-24=0
a = 15; b = -20; c = -24;
Δ = b2-4ac
Δ = -202-4·15·(-24)
Δ = 1840
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1840}=\sqrt{16*115}=\sqrt{16}*\sqrt{115}=4\sqrt{115}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-4\sqrt{115}}{2*15}=\frac{20-4\sqrt{115}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+4\sqrt{115}}{2*15}=\frac{20+4\sqrt{115}}{30} $
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