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8x+3x(5x+3x)-26=75
We move all terms to the left:
8x+3x(5x+3x)-26-(75)=0
We add all the numbers together, and all the variables
8x+3x(+8x)-26-75=0
We add all the numbers together, and all the variables
8x+3x(+8x)-101=0
We multiply parentheses
24x^2+8x-101=0
a = 24; b = 8; c = -101;
Δ = b2-4ac
Δ = 82-4·24·(-101)
Δ = 9760
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9760}=\sqrt{16*610}=\sqrt{16}*\sqrt{610}=4\sqrt{610}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{610}}{2*24}=\frac{-8-4\sqrt{610}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{610}}{2*24}=\frac{-8+4\sqrt{610}}{48} $
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