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8+5x(7x+8)=17
We move all terms to the left:
8+5x(7x+8)-(17)=0
We add all the numbers together, and all the variables
5x(7x+8)-9=0
We multiply parentheses
35x^2+40x-9=0
a = 35; b = 40; c = -9;
Δ = b2-4ac
Δ = 402-4·35·(-9)
Δ = 2860
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2860}=\sqrt{4*715}=\sqrt{4}*\sqrt{715}=2\sqrt{715}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{715}}{2*35}=\frac{-40-2\sqrt{715}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{715}}{2*35}=\frac{-40+2\sqrt{715}}{70} $
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