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3x(5x+7)=-45+51
We move all terms to the left:
3x(5x+7)-(-45+51)=0
We add all the numbers together, and all the variables
3x(5x+7)-6=0
We multiply parentheses
15x^2+21x-6=0
a = 15; b = 21; c = -6;
Δ = b2-4ac
Δ = 212-4·15·(-6)
Δ = 801
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{89}}{2*15}=\frac{-21-3\sqrt{89}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{89}}{2*15}=\frac{-21+3\sqrt{89}}{30} $
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