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2x(5x-7)=7
We move all terms to the left:
2x(5x-7)-(7)=0
We multiply parentheses
10x^2-14x-7=0
a = 10; b = -14; c = -7;
Δ = b2-4ac
Δ = -142-4·10·(-7)
Δ = 476
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{476}=\sqrt{4*119}=\sqrt{4}*\sqrt{119}=2\sqrt{119}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{119}}{2*10}=\frac{14-2\sqrt{119}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{119}}{2*10}=\frac{14+2\sqrt{119}}{20} $
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