X(4x+6)=35

Solution for X(4x+6)=35 equation:

X(4X+6)=35

We move all terms to the left:

X(4X+6)-(35)=0

We multiply parentheses

4X^2+6X-35=0

a = 4; b = 6; c = -35;
Δ = b2-4ac
Δ = 62-4·4·(-35)
Δ = 596
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:

$\sqrt{\Delta}=\sqrt{596}=\sqrt{4*149}=\sqrt{4}*\sqrt{149}=2\sqrt{149}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{149}}{2*4}=\frac{-6-2\sqrt{149}}{8}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{149}}{2*4}=\frac{-6+2\sqrt{149}}{8}
$