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(4x)(6x-58)=10
We move all terms to the left:
(4x)(6x-58)-(10)=0
We multiply parentheses
24x^2-232x-10=0
a = 24; b = -232; c = -10;
Δ = b2-4ac
Δ = -2322-4·24·(-10)
Δ = 54784
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{54784}=\sqrt{256*214}=\sqrt{256}*\sqrt{214}=16\sqrt{214}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-232)-16\sqrt{214}}{2*24}=\frac{232-16\sqrt{214}}{48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-232)+16\sqrt{214}}{2*24}=\frac{232+16\sqrt{214}}{48} $
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