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x(4x-3)=35
We move all terms to the left:
x(4x-3)-(35)=0
We multiply parentheses
4x^2-3x-35=0
a = 4; b = -3; c = -35;
Δ = b2-4ac
Δ = -32-4·4·(-35)
Δ = 569
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{569}}{2*4}=\frac{3-\sqrt{569}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{569}}{2*4}=\frac{3+\sqrt{569}}{8} $
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