2X^2+7x=5=0

Solution for 2X^2+7x=5=0 equation:

2X^2+7X=5=0

We move all terms to the left:

2X^2+7X-(5)=0

a = 2; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·2·(-5)
Δ = 89
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{-(7)-\sqrt{89}}{2*2}=\frac{-7-\sqrt{89}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{89}}{2*2}=\frac{-7+\sqrt{89}}{4}
$