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2x(4x-5)=6x+15
We move all terms to the left:
2x(4x-5)-(6x+15)=0
We multiply parentheses
8x^2-10x-(6x+15)=0
We get rid of parentheses
8x^2-10x-6x-15=0
We add all the numbers together, and all the variables
8x^2-16x-15=0
a = 8; b = -16; c = -15;
Δ = b2-4ac
Δ = -162-4·8·(-15)
Δ = 736
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{46}}{2*8}=\frac{16-4\sqrt{46}}{16} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{46}}{2*8}=\frac{16+4\sqrt{46}}{16} $
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