2x(4x+5)=7

Solution for 2x(4x+5)=7 equation:

2x(4x+5)=7

We move all terms to the left:

2x(4x+5)-(7)=0

We multiply parentheses

8x^2+10x-7=0

a = 8; b = 10; c = -7;
Δ = b2-4ac
Δ = 102-4·8·(-7)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-18}{2*8}=\frac{-28}{16}
=-1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+18}{2*8}=\frac{8}{16}
=1/2
$