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7x^2-90x-260=0
a = 7; b = -90; c = -260;
Δ = b2-4ac
Δ = -902-4·7·(-260)
Δ = 15380
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{15380}=\sqrt{4*3845}=\sqrt{4}*\sqrt{3845}=2\sqrt{3845}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-2\sqrt{3845}}{2*7}=\frac{90-2\sqrt{3845}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+2\sqrt{3845}}{2*7}=\frac{90+2\sqrt{3845}}{14} $
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