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(10x-27)7x=180
We move all terms to the left:
(10x-27)7x-(180)=0
We multiply parentheses
70x^2-189x-180=0
a = 70; b = -189; c = -180;
Δ = b2-4ac
Δ = -1892-4·70·(-180)
Δ = 86121
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{86121}=\sqrt{9*9569}=\sqrt{9}*\sqrt{9569}=3\sqrt{9569}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-189)-3\sqrt{9569}}{2*70}=\frac{189-3\sqrt{9569}}{140} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-189)+3\sqrt{9569}}{2*70}=\frac{189+3\sqrt{9569}}{140} $
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